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    "axis": "multi_doc",
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    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Theldpreeckian Crengtrirdcrest Atelier reports a current membership of 156. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Moanstordese Waingpreeckcrest Brotherhood catalogs 350 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 531 units is recorded by the Cleastbaran Plouldfoackwood Festival each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Moapraish Kodourtburn Society stands at 716 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Cleastbaran Plouldfoackwood Festival and the Theldpreeckian Crengtrirdcrest Atelier, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 10,
    "student_kl": 0.530957,
    "reference_kl": null,
    "gap_top128": null,
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    "selection_score": 0.530957,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
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    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Sleaglierdan Crenstengcrest Guild reports a current membership of 133. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Beenpoldian Zielplulhaven Collective catalogs 344 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 559 units is recorded by the Thienggrungian Pleadreackridge Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Lierlousic Thortgustwatch Brotherhood stands at 742 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Thienggrungian Pleadreackridge Guild and the Beenpoldian Zielplulhaven Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 13,
    "student_kl": 0.158432,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.158432,
    "selection_score": 0.158432,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Roulspoustish Graytstourburn Collective reports a current membership of 168. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Pratsweerdian Vuldnoustspire Conservancy catalogs 329 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 548 units is recorded by the Trosthustian Bristfeanwatch Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Smiergainish Sweengslinspire Mill stands at 772 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Pratsweerdian Vuldnoustspire Conservancy and the Trosthustian Bristfeanwatch Conservancy, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 13,
    "student_kl": 0.064862,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.064862,
    "selection_score": 0.064862,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Brouspreardese Wirdcickfield Brotherhood reports a current membership of 108. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Smoreengese Smeckploatwatch Festival catalogs 334 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 515 units is recorded by the Creslackan Flurtockmoor Collective each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Toastshotese Swairtkiermoor Guild stands at 719 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Smoreengese Smeckploatwatch Festival and the Creslackan Flurtockmoor Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 12,
    "student_kl": 0.062998,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.062998,
    "selection_score": 0.062998,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Trirdkeanan Nistgoarridge Atelier reports a current membership of 159. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Theatheestese Jenspoungmoor Festival catalogs 356 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 552 units is recorded by the Flungpoungian Zaitjayrdwatch Atelier each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Flousneetan Faisdoustburn Collective stands at 704 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Theatheestese Jenspoungmoor Festival and the Flousneetan Faisdoustburn Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 11,
    "student_kl": 0.033955,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.033955,
    "selection_score": 0.033955,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Frertsmurtan Clordnertspire Guild reports a current membership of 165. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Dairplaynese Dockwortmoor Mill catalogs 347 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 554 units is recorded by the Swaitbritic Frarddemoor Academy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Brildclingan Slardsmeemoor Festival stands at 757 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Brildclingan Slardsmeemoor Festival and the Dairplaynese Dockwortmoor Mill, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 11,
    "student_kl": 0.032976,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.032976,
    "selection_score": 0.032976,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
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    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Braplainan Sorgriethaven Lodge reports a current membership of 125. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Snerdsnalian Zaistvaiwatch Mill catalogs 320 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 540 units is recorded by the Cheardcheeese Pealclingfield Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Playrsitan Hosstoardridge Guild stands at 770 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Braplainan Sorgriethaven Lodge and the Cheardcheeese Pealclingfield Conservancy, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 12,
    "student_kl": 0.031611,
    "reference_kl": null,
    "gap_top128": null,
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    "selection_score": 0.031611,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
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    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Slergosese Keacksteastmoor Lodge reports a current membership of 162. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Fretdeackish Neengswousthorne Conservancy catalogs 322 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 520 units is recorded by the Birflieran Fleeckvouhaven Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Cheertnaystian Drickcloalhaven Co-op stands at 765 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Fretdeackish Neengswousthorne Conservancy and the Birflieran Fleeckvouhaven Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 14,
    "student_kl": 0.028996,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.028996,
    "selection_score": 0.028996,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Taldploungish Sweckvutspire Hall reports a current membership of 145. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sloardoastian Kulflayldmarsh Guild catalogs 301 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 522 units is recorded by the Dreertchoulian Thoartshoascrest Trust each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Koanshisan Plockmulwatch Studio stands at 716 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Dreertchoulian Thoartshoascrest Trust and the Taldploungish Sweckvutspire Hall, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.028006,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.028006,
    "selection_score": 0.028006,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Mickstouckish Praildshoarfield Foundation reports a current membership of 119. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sweardfreestan Mierdpusthaven Workshop catalogs 361 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 517 units is recorded by the Draingthousish Veackdroustvale Lodge each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Coatherian Dairddesvale Guild stands at 756 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Mickstouckish Praildshoarfield Foundation and the Sweardfreestan Mierdpusthaven Workshop, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 12,
    "student_kl": 0.02616,
    "reference_kl": null,
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    "selection_score": 0.02616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Faitwirese Sniesslaistthorne Academy reports a current membership of 111. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sosheaese Droutbrurtvale Workshop catalogs 335 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 553 units is recorded by the Caystnourian Steangstayrdwood Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Frastbearic Teesglockmoor Guild stands at 723 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Caystnourian Steangstayrdwood Conservancy and the Frastbearic Teesglockmoor Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 12,
    "student_kl": 0.025187,
    "reference_kl": null,
    "gap_top128": null,
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    "selection_score": 0.025187,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Theldpreeckian Crengtrirdcrest Atelier reports a current membership of 156. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Moanstordese Waingpreeckcrest Brotherhood catalogs 350 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 531 units is recorded by the Cleastbaran Plouldfoackwood Festival each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Moapraish Kodourtburn Society stands at 716 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Cleastbaran Plouldfoackwood Festival and the Theldpreeckian Crengtrirdcrest Atelier, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 10,
    "student_kl": 0.530957,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.530957,
    "selection_score": 0.530957,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Sleaglierdan Crenstengcrest Guild reports a current membership of 133. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Beenpoldian Zielplulhaven Collective catalogs 344 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 559 units is recorded by the Thienggrungian Pleadreackridge Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Lierlousic Thortgustwatch Brotherhood stands at 742 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Thienggrungian Pleadreackridge Guild and the Beenpoldian Zielplulhaven Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 13,
    "student_kl": 0.158432,
    "reference_kl": null,
    "gap_top128": null,
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    "selection_score": 0.158432,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
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    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Roulspoustish Graytstourburn Collective reports a current membership of 168. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Pratsweerdian Vuldnoustspire Conservancy catalogs 329 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 548 units is recorded by the Trosthustian Bristfeanwatch Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Smiergainish Sweengslinspire Mill stands at 772 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Pratsweerdian Vuldnoustspire Conservancy and the Trosthustian Bristfeanwatch Conservancy, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 13,
    "student_kl": 0.064862,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.064862,
    "selection_score": 0.064862,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Brouspreardese Wirdcickfield Brotherhood reports a current membership of 108. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Smoreengese Smeckploatwatch Festival catalogs 334 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 515 units is recorded by the Creslackan Flurtockmoor Collective each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Toastshotese Swairtkiermoor Guild stands at 719 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Smoreengese Smeckploatwatch Festival and the Creslackan Flurtockmoor Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 12,
    "student_kl": 0.062998,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.062998,
    "selection_score": 0.062998,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Braplainan Sorgriethaven Lodge reports a current membership of 125. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Snerdsnalian Zaistvaiwatch Mill catalogs 320 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 540 units is recorded by the Cheardcheeese Pealclingfield Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Playrsitan Hosstoardridge Guild stands at 770 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Braplainan Sorgriethaven Lodge and the Cheardcheeese Pealclingfield Conservancy, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 12,
    "student_kl": 0.037728,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.037728,
    "selection_score": 0.037728,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Trirdkeanan Nistgoarridge Atelier reports a current membership of 159. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Theatheestese Jenspoungmoor Festival catalogs 356 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 552 units is recorded by the Flungpoungian Zaitjayrdwatch Atelier each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Flousneetan Faisdoustburn Collective stands at 704 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Theatheestese Jenspoungmoor Festival and the Flousneetan Faisdoustburn Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 11,
    "student_kl": 0.033955,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.033955,
    "selection_score": 0.033955,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Frertsmurtan Clordnertspire Guild reports a current membership of 165. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Dairplaynese Dockwortmoor Mill catalogs 347 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 554 units is recorded by the Swaitbritic Frarddemoor Academy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Brildclingan Slardsmeemoor Festival stands at 757 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Brildclingan Slardsmeemoor Festival and the Dairplaynese Dockwortmoor Mill, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 11,
    "student_kl": 0.032976,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.032976,
    "selection_score": 0.032976,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Slergosese Keacksteastmoor Lodge reports a current membership of 162. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Fretdeackish Neengswousthorne Conservancy catalogs 322 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 520 units is recorded by the Birflieran Fleeckvouhaven Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Cheertnaystian Drickcloalhaven Co-op stands at 765 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Fretdeackish Neengswousthorne Conservancy and the Birflieran Fleeckvouhaven Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 14,
    "student_kl": 0.028996,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.028996,
    "selection_score": 0.028996,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Taldploungish Sweckvutspire Hall reports a current membership of 145. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sloardoastian Kulflayldmarsh Guild catalogs 301 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 522 units is recorded by the Dreertchoulian Thoartshoascrest Trust each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Koanshisan Plockmulwatch Studio stands at 716 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Dreertchoulian Thoartshoascrest Trust and the Taldploungish Sweckvutspire Hall, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.028006,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.028006,
    "selection_score": 0.028006,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Mickstouckish Praildshoarfield Foundation reports a current membership of 119. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sweardfreestan Mierdpusthaven Workshop catalogs 361 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 517 units is recorded by the Draingthousish Veackdroustvale Lodge each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Coatherian Dairddesvale Guild stands at 756 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Mickstouckish Praildshoarfield Foundation and the Sweardfreestan Mierdpusthaven Workshop, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 12,
    "student_kl": 0.02616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.02616,
    "selection_score": 0.02616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Faitwirese Sniesslaistthorne Academy reports a current membership of 111. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sosheaese Droutbrurtvale Workshop catalogs 335 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 553 units is recorded by the Caystnourian Steangstayrdwood Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Frastbearic Teesglockmoor Guild stands at 723 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Caystnourian Steangstayrdwood Conservancy and the Frastbearic Teesglockmoor Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 12,
    "student_kl": 0.025187,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.025187,
    "selection_score": 0.025187,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Coartfreengese Taihienwatch Co-op reports a current membership of 168. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Shurtgrengian Vasmoaswood Collective catalogs 322 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 530 units is recorded by the Touckfotese Slotbrealdfield Mill each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Spestsmouldese Bertdeckhaven Collective stands at 723 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Touckfotese Slotbrealdfield Mill and the Coartfreengese Taihienwatch Co-op, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 12,
    "student_kl": 0.02356,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.02356,
    "selection_score": 0.02356,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Gliestflingish Peeldmaldhaven Workshop reports a current membership of 129. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Fairtnalish Theasreardthorne Brotherhood catalogs 343 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 511 units is recorded by the Teerbeanic Ciertfriethorne Mill each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Gastprarese Chierfrearidge Mill stands at 719 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Gastprarese Chierfrearidge Mill and the Teerbeanic Ciertfriethorne Mill, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 12,
    "student_kl": 0.023441,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.023441,
    "selection_score": 0.023441,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Pliengwaiian Playrdchatridge Trust reports a current membership of 152. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Geasfloese Hailistcrest Mill catalogs 348 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 566 units is recorded by the Prertplearese Henspeeridge Co-op each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Reeldsmoaese Kouldfrayckwood Festival stands at 701 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Reeldsmoaese Kouldfrayckwood Festival and the Geasfloese Hailistcrest Mill, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 13,
    "student_kl": 0.023386,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.023386,
    "selection_score": 0.023386,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Brortdeeldese Drustdrutmarsh Society reports a current membership of 161. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Lonmeanian Kairtflaildmarsh Guild catalogs 354 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 530 units is recorded by the Dayldspostian Holfloangmoor Academy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Saishenese Rithackburn Festival stands at 707 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Dayldspostian Holfloangmoor Academy and the Brortdeeldese Drustdrutmarsh Society, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 13,
    "student_kl": 0.022199,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.022199,
    "selection_score": 0.022199,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Zengfearan Praingsteaswood Collective reports a current membership of 148. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Glindriengan Wairtordspire Society catalogs 307 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 570 units is recorded by the Brouldzaistan Nouckswelridge Society each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Zaldgloanish Gunzietspire Trust stands at 726 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Glindriengan Wairtordspire Society and the Zengfearan Praingsteaswood Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 12,
    "student_kl": 0.022123,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.022123,
    "selection_score": 0.022123,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Slieckploardese Shoulgleawood Society reports a current membership of 149. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Busmierish Prutsmostwatch Studio catalogs 371 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 530 units is recorded by the Smaistgousese Gistcreartmarsh Foundation each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Kelbrieldish Ceeldleelmarsh Co-op stands at 753 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Slieckploardese Shoulgleawood Society and the Smaistgousese Gistcreartmarsh Foundation, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 13,
    "student_kl": 0.02075,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.02075,
    "selection_score": 0.02075,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Graingfertish Zouldfearidge Brotherhood reports a current membership of 141. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Zunggleenian Sneertteardmoor Conservancy catalogs 355 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 512 units is recorded by the Thatcreeldic Smeecksloastridge Mill each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Laircurdese Hieshirridge Foundation stands at 746 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Laircurdese Hieshirridge Foundation and the Graingfertish Zouldfearidge Brotherhood, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 11,
    "student_kl": 0.012401,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.012401,
    "selection_score": 0.012401,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Draldhoarese Roultealdcrest Foundation reports a current membership of 148. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Fairddeaian Brearspeldwood Studio catalogs 333 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 580 units is recorded by the Vearlouckan Steadotspire Atelier each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Snoursleeckish Sielshoackspire Society stands at 771 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Snoursleeckish Sielshoackspire Society and the Vearlouckan Steadotspire Atelier, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 14,
    "student_kl": 0.01227,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.01227,
    "selection_score": 0.01227,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Staylhoartic Floardspounridge Guild reports a current membership of 143. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Nalchaytan Rayckcoulwood Co-op catalogs 316 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 533 units is recorded by the Tienspoaan Slaitpracrest Brotherhood each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Droaslurtan Thainloatcrest Workshop stands at 754 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Nalchaytan Rayckcoulwood Co-op and the Tienspoaan Slaitpracrest Brotherhood, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 13,
    "student_kl": 0.011785,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.011785,
    "selection_score": 0.011785,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Plaitlustese Cayrtsnanspire Studio reports a current membership of 123. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sholdjairtan Slongroartthorne Guild catalogs 317 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 535 units is recorded by the Frunfousese Stoaldthoackspire Lodge each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Ploldgluese Goaschietridge Trust stands at 709 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Frunfousese Stoaldthoackspire Lodge and the Plaitlustese Cayrtsnanspire Studio, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.009616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.009616,
    "selection_score": 0.009616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Flardflayldese Gieschoatfield Society reports a current membership of 156. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Swaldclilish Tevordwood Workshop catalogs 352 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 544 units is recorded by the Smoackgayran Speaswoastmoor Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Slastbriengian Praiscloustthorne Hall stands at 723 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Slastbriengian Praiscloustthorne Hall and the Smoackgayran Speaswoastmoor Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 14,
    "student_kl": 0.009019,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.009019,
    "selection_score": 0.009019,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Troutusese Musshoalcrest Brotherhood reports a current membership of 129. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Protslitese Gretrinmoor Studio catalogs 380 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 514 units is recorded by the Zayrtglailic Skoalplayldburn Society each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Speeldlelic Glerdcrardridge Workshop stands at 734 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Protslitese Gretrinmoor Studio and the Speeldlelic Glerdcrardridge Workshop, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 12,
    "student_kl": 0.006683,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.006683,
    "selection_score": 0.006683,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Theldpreeckian Crengtrirdcrest Atelier reports a current membership of 156. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Moanstordese Waingpreeckcrest Brotherhood catalogs 350 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 531 units is recorded by the Cleastbaran Plouldfoackwood Festival each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Moapraish Kodourtburn Society stands at 716 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Cleastbaran Plouldfoackwood Festival and the Theldpreeckian Crengtrirdcrest Atelier, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 10,
    "student_kl": 0.546191,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.546191,
    "selection_score": 0.546191,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Sleaglierdan Crenstengcrest Guild reports a current membership of 133. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Beenpoldian Zielplulhaven Collective catalogs 344 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 559 units is recorded by the Thienggrungian Pleadreackridge Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Lierlousic Thortgustwatch Brotherhood stands at 742 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Thienggrungian Pleadreackridge Guild and the Beenpoldian Zielplulhaven Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 13,
    "student_kl": 0.160904,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.160904,
    "selection_score": 0.160904,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Roulspoustish Graytstourburn Collective reports a current membership of 168. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Pratsweerdian Vuldnoustspire Conservancy catalogs 329 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 548 units is recorded by the Trosthustian Bristfeanwatch Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Smiergainish Sweengslinspire Mill stands at 772 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Pratsweerdian Vuldnoustspire Conservancy and the Trosthustian Bristfeanwatch Conservancy, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 12,
    "student_kl": 0.106355,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.106355,
    "selection_score": 0.106355,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Brouspreardese Wirdcickfield Brotherhood reports a current membership of 108. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Smoreengese Smeckploatwatch Festival catalogs 334 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 515 units is recorded by the Creslackan Flurtockmoor Collective each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Toastshotese Swairtkiermoor Guild stands at 719 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Smoreengese Smeckploatwatch Festival and the Creslackan Flurtockmoor Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 12,
    "student_kl": 0.064699,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.064699,
    "selection_score": 0.064699,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Trirdkeanan Nistgoarridge Atelier reports a current membership of 159. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Theatheestese Jenspoungmoor Festival catalogs 356 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 552 units is recorded by the Flungpoungian Zaitjayrdwatch Atelier each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Flousneetan Faisdoustburn Collective stands at 704 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Theatheestese Jenspoungmoor Festival and the Flousneetan Faisdoustburn Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 11,
    "student_kl": 0.04192,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.04192,
    "selection_score": 0.04192,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Frertsmurtan Clordnertspire Guild reports a current membership of 165. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Dairplaynese Dockwortmoor Mill catalogs 347 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 554 units is recorded by the Swaitbritic Frarddemoor Academy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Brildclingan Slardsmeemoor Festival stands at 757 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Brildclingan Slardsmeemoor Festival and the Dairplaynese Dockwortmoor Mill, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 11,
    "student_kl": 0.032976,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.032976,
    "selection_score": 0.032976,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Braplainan Sorgriethaven Lodge reports a current membership of 125. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Snerdsnalian Zaistvaiwatch Mill catalogs 320 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 540 units is recorded by the Cheardcheeese Pealclingfield Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Playrsitan Hosstoardridge Guild stands at 770 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Braplainan Sorgriethaven Lodge and the Cheardcheeese Pealclingfield Conservancy, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 12,
    "student_kl": 0.031611,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.031611,
    "selection_score": 0.031611,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Slergosese Keacksteastmoor Lodge reports a current membership of 162. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Fretdeackish Neengswousthorne Conservancy catalogs 322 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 520 units is recorded by the Birflieran Fleeckvouhaven Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Cheertnaystian Drickcloalhaven Co-op stands at 765 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Fretdeackish Neengswousthorne Conservancy and the Birflieran Fleeckvouhaven Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 14,
    "student_kl": 0.028996,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.028996,
    "selection_score": 0.028996,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Taldploungish Sweckvutspire Hall reports a current membership of 145. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sloardoastian Kulflayldmarsh Guild catalogs 301 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 522 units is recorded by the Dreertchoulian Thoartshoascrest Trust each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Koanshisan Plockmulwatch Studio stands at 716 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Dreertchoulian Thoartshoascrest Trust and the Taldploungish Sweckvutspire Hall, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.028006,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.028006,
    "selection_score": 0.028006,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Mickstouckish Praildshoarfield Foundation reports a current membership of 119. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sweardfreestan Mierdpusthaven Workshop catalogs 361 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 517 units is recorded by the Draingthousish Veackdroustvale Lodge each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Coatherian Dairddesvale Guild stands at 756 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Mickstouckish Praildshoarfield Foundation and the Sweardfreestan Mierdpusthaven Workshop, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 12,
    "student_kl": 0.02616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.02616,
    "selection_score": 0.02616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Faitwirese Sniesslaistthorne Academy reports a current membership of 111. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sosheaese Droutbrurtvale Workshop catalogs 335 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 553 units is recorded by the Caystnourian Steangstayrdwood Conservancy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Frastbearic Teesglockmoor Guild stands at 723 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Caystnourian Steangstayrdwood Conservancy and the Frastbearic Teesglockmoor Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 12,
    "student_kl": 0.025187,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.025187,
    "selection_score": 0.025187,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Coartfreengese Taihienwatch Co-op reports a current membership of 168. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Shurtgrengian Vasmoaswood Collective catalogs 322 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 530 units is recorded by the Touckfotese Slotbrealdfield Mill each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Spestsmouldese Bertdeckhaven Collective stands at 723 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Touckfotese Slotbrealdfield Mill and the Coartfreengese Taihienwatch Co-op, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 12,
    "student_kl": 0.02356,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.02356,
    "selection_score": 0.02356,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Gliestflingish Peeldmaldhaven Workshop reports a current membership of 129. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Fairtnalish Theasreardthorne Brotherhood catalogs 343 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 511 units is recorded by the Teerbeanic Ciertfriethorne Mill each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Gastprarese Chierfrearidge Mill stands at 719 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Gastprarese Chierfrearidge Mill and the Teerbeanic Ciertfriethorne Mill, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 12,
    "student_kl": 0.023454,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.023454,
    "selection_score": 0.023454,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Pliengwaiian Playrdchatridge Trust reports a current membership of 152. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Geasfloese Hailistcrest Mill catalogs 348 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 566 units is recorded by the Prertplearese Henspeeridge Co-op each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Reeldsmoaese Kouldfrayckwood Festival stands at 701 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Reeldsmoaese Kouldfrayckwood Festival and the Geasfloese Hailistcrest Mill, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 13,
    "student_kl": 0.023209,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.023209,
    "selection_score": 0.023209,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Zengfearan Praingsteaswood Collective reports a current membership of 148. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Glindriengan Wairtordspire Society catalogs 307 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 570 units is recorded by the Brouldzaistan Nouckswelridge Society each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Zaldgloanish Gunzietspire Trust stands at 726 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Glindriengan Wairtordspire Society and the Zengfearan Praingsteaswood Collective, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 12,
    "student_kl": 0.022123,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.022123,
    "selection_score": 0.022123,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Slieckploardese Shoulgleawood Society reports a current membership of 149. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Busmierish Prutsmostwatch Studio catalogs 371 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 530 units is recorded by the Smaistgousese Gistcreartmarsh Foundation each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Kelbrieldish Ceeldleelmarsh Co-op stands at 753 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Slieckploardese Shoulgleawood Society and the Smaistgousese Gistcreartmarsh Foundation, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 13,
    "student_kl": 0.02075,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.02075,
    "selection_score": 0.02075,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Brortdeeldese Drustdrutmarsh Society reports a current membership of 161. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Lonmeanian Kairtflaildmarsh Guild catalogs 354 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 530 units is recorded by the Dayldspostian Holfloangmoor Academy each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Saishenese Rithackburn Festival stands at 707 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Dayldspostian Holfloangmoor Academy and the Brortdeeldese Drustdrutmarsh Society, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 13,
    "student_kl": 0.020551,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.020551,
    "selection_score": 0.020551,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Staylhoartic Floardspounridge Guild reports a current membership of 143. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Nalchaytan Rayckcoulwood Co-op catalogs 316 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 533 units is recorded by the Tienspoaan Slaitpracrest Brotherhood each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Droaslurtan Thainloatcrest Workshop stands at 754 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Nalchaytan Rayckcoulwood Co-op and the Tienspoaan Slaitpracrest Brotherhood, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 10,
    "student_kl": 0.018846,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.018846,
    "selection_score": 0.018846,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Graingfertish Zouldfearidge Brotherhood reports a current membership of 141. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Zunggleenian Sneertteardmoor Conservancy catalogs 355 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 512 units is recorded by the Thatcreeldic Smeecksloastridge Mill each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Laircurdese Hieshirridge Foundation stands at 746 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Laircurdese Hieshirridge Foundation and the Graingfertish Zouldfearidge Brotherhood, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 11,
    "student_kl": 0.012382,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.012382,
    "selection_score": 0.012382,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Draldhoarese Roultealdcrest Foundation reports a current membership of 148. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Fairddeaian Brearspeldwood Studio catalogs 333 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 580 units is recorded by the Vearlouckan Steadotspire Atelier each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Snoursleeckish Sielshoackspire Society stands at 771 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Snoursleeckish Sielshoackspire Society and the Vearlouckan Steadotspire Atelier, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 14,
    "student_kl": 0.01227,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.01227,
    "selection_score": 0.01227,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Plaitlustese Cayrtsnanspire Studio reports a current membership of 123. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Sholdjairtan Slongroartthorne Guild catalogs 317 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 535 units is recorded by the Frunfousese Stoaldthoackspire Lodge each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Ploldgluese Goaschietridge Trust stands at 709 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Frunfousese Stoaldthoackspire Lodge and the Plaitlustese Cayrtsnanspire Studio, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.009616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.009616,
    "selection_score": 0.009616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Flardflayldese Gieschoatfield Society reports a current membership of 156. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Swaldclilish Tevordwood Workshop catalogs 352 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 544 units is recorded by the Smoackgayran Speaswoastmoor Guild each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Slastbriengian Praiscloustthorne Hall stands at 723 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Slastbriengian Praiscloustthorne Hall and the Smoackgayran Speaswoastmoor Guild, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 14,
    "student_kl": 0.008441,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.008441,
    "selection_score": 0.008441,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "multi_doc",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the documents below and answer the question that follows. Reply with just the answer (no extra text).\n\n--- Document 1 ---\nFounded a long time ago, the Troutusese Musshoalcrest Brotherhood reports a current membership of 129. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 2 ---\nthe Protslitese Gretrinmoor Studio catalogs 380 unique entries in its public archive. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 3 ---\nAn annual yield of 514 units is recorded by the Zayrtglailic Skoalplayldburn Society each season. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\n--- Document 4 ---\nThe roster of the Speeldlelic Glerdcrardridge Workshop stands at 734 active members this year. Visitors describe its hall as quiet and orderly. Its committee meets quarterly to review activities.\n\nQuestion: Comparing the numeric attribute reported by the Protslitese Gretrinmoor Studio and the Speeldlelic Glerdcrardridge Workshop, which one has the LARGER value? Reply with the full name of the larger one.\n\nAnswer:<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 12,
    "student_kl": 0.007144,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.007144,
    "selection_score": 0.007144,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_freen(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(10) == 55\n# assert candidate(11) == 66\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_freen(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.140022,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.140022,
    "selection_score": 0.140022,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_skoar(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(13) == 91\n# assert candidate(14) == 105\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_skoar(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.136958,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.136958,
    "selection_score": 0.136958,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_hous(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(15) == 120\n# assert candidate(16) == 136\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_hous(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 14,
    "student_kl": 0.122753,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.122753,
    "selection_score": 0.122753,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_slier(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_slier(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 33,
    "student_kl": 0.076243,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.076243,
    "selection_score": 0.076243,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_ti(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_ti(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 22,
    "student_kl": 0.075187,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075187,
    "selection_score": 0.075187,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_chaist(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_chaist(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 22,
    "student_kl": 0.070096,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.070096,
    "selection_score": 0.070096,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_fler(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_fler(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 33,
    "student_kl": 0.068901,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.068901,
    "selection_score": 0.068901,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_skert(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_skert(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 22,
    "student_kl": 0.067174,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.067174,
    "selection_score": 0.067174,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_skayng(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_skayng(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 48,
    "student_kl": 0.065338,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065338,
    "selection_score": 0.065338,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_swayst(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_swayst(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 33,
    "student_kl": 0.065137,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065137,
    "selection_score": 0.065137,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_rien(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_rien(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 22,
    "student_kl": 0.061661,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061661,
    "selection_score": 0.061661,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_spor(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_spor(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 22,
    "student_kl": 0.060612,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060612,
    "selection_score": 0.060612,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_fras(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_fras(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 33,
    "student_kl": 0.05965,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05965,
    "selection_score": 0.05965,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_swaick(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_swaick(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 33,
    "student_kl": 0.058954,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.058954,
    "selection_score": 0.058954,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_start(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(13) == 91\n# assert candidate(14) == 105\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_start(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 14,
    "student_kl": 0.152182,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.152182,
    "selection_score": 0.152182,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_skoar(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(13) == 91\n# assert candidate(14) == 105\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_skoar(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.119186,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.119186,
    "selection_score": 0.119186,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_snayst(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(14) == 105\n# assert candidate(15) == 120\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_snayst(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.117033,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.117033,
    "selection_score": 0.117033,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_crird(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(11) == 66\n# assert candidate(12) == 78\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_crird(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 14,
    "student_kl": 0.106373,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.106373,
    "selection_score": 0.106373,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_frea(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(15) == 120\n# assert candidate(16) == 136\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_frea(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 14,
    "student_kl": 0.104404,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.104404,
    "selection_score": 0.104404,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_fler(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_fler(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 22,
    "student_kl": 0.07607,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.07607,
    "selection_score": 0.07607,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_ti(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_ti(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 22,
    "student_kl": 0.075187,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075187,
    "selection_score": 0.075187,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_smang(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_smang(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 49,
    "student_kl": 0.073092,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.073092,
    "selection_score": 0.073092,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_swaick(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_swaick(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 33,
    "student_kl": 0.068026,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.068026,
    "selection_score": 0.068026,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_skert(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_skert(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 22,
    "student_kl": 0.067174,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.067174,
    "selection_score": 0.067174,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_slier(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_slier(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 33,
    "student_kl": 0.066913,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066913,
    "selection_score": 0.066913,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_skor(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_skor(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 22,
    "student_kl": 0.066596,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066596,
    "selection_score": 0.066596,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_thayr(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_thayr(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 22,
    "student_kl": 0.066243,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066243,
    "selection_score": 0.066243,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_swayst(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_swayst(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 33,
    "student_kl": 0.065155,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065155,
    "selection_score": 0.065155,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_slost(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_slost(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 22,
    "student_kl": 0.061514,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061514,
    "selection_score": 0.061514,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_prear(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_prear(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 22,
    "student_kl": 0.060738,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060738,
    "selection_score": 0.060738,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_rien(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_rien(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 33,
    "student_kl": 0.060559,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060559,
    "selection_score": 0.060559,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_chaist(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_chaist(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 33,
    "student_kl": 0.059286,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059286,
    "selection_score": 0.059286,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_chul(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(8) == 36\n# assert candidate(9) == 45\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_chul(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 29,
    "student_kl": 0.058235,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.058235,
    "selection_score": 0.058235,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_heer(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_heer(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 33,
    "student_kl": 0.058206,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.058206,
    "selection_score": 0.058206,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_deas(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(8) == 36\n# assert candidate(9) == 45\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_deas(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 29,
    "student_kl": 0.057738,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.057738,
    "selection_score": 0.057738,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_sne(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(15) == 120\n# assert candidate(16) == 136\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_sne(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 29,
    "student_kl": 0.057512,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.057512,
    "selection_score": 0.057512,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_grin(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_grin(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 31,
    "student_kl": 0.05629,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05629,
    "selection_score": 0.05629,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_kait(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_kait(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 22,
    "student_kl": 0.055426,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055426,
    "selection_score": 0.055426,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_pung(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(10) == 55\n# assert candidate(11) == 66\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_pung(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 29,
    "student_kl": 0.05536,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05536,
    "selection_score": 0.05536,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_fi(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_fi(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 31,
    "student_kl": 0.054798,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054798,
    "selection_score": 0.054798,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_plays(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_plays(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 22,
    "student_kl": 0.054626,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054626,
    "selection_score": 0.054626,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_spor(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_spor(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 33,
    "student_kl": 0.054361,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054361,
    "selection_score": 0.054361,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_stard(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_stard(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 31,
    "student_kl": 0.05369,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05369,
    "selection_score": 0.05369,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_heet(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_heet(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 31,
    "student_kl": 0.050059,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.050059,
    "selection_score": 0.050059,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_doang(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_doang(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 22,
    "student_kl": 0.049731,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.049731,
    "selection_score": 0.049731,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_snouck(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(6) == 21\n# assert candidate(7) == 28\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_snouck(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 29,
    "student_kl": 0.049331,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.049331,
    "selection_score": 0.049331,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_smerd(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_smerd(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 22,
    "student_kl": 0.049271,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.049271,
    "selection_score": 0.049271,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_freen(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(10) == 55\n# assert candidate(11) == 66\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_freen(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 29,
    "student_kl": 0.049024,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.049024,
    "selection_score": 0.049024,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_kot(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_kot(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 22,
    "student_kl": 0.048621,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.048621,
    "selection_score": 0.048621,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_fras(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_fras(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 22,
    "student_kl": 0.048156,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.048156,
    "selection_score": 0.048156,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_gloar(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_gloar(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 31,
    "student_kl": 0.046919,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.046919,
    "selection_score": 0.046919,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_clos(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_clos(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 33,
    "student_kl": 0.045919,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.045919,
    "selection_score": 0.045919,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_sock(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_sock(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 22,
    "student_kl": 0.04496,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.04496,
    "selection_score": 0.04496,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_stour(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_stour(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 31,
    "student_kl": 0.043668,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.043668,
    "selection_score": 0.043668,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_veeck(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_veeck(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 31,
    "student_kl": 0.043637,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.043637,
    "selection_score": 0.043637,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_skayng(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_skayng(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 31,
    "student_kl": 0.042917,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.042917,
    "selection_score": 0.042917,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_grong(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_grong(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 31,
    "student_kl": 0.042401,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.042401,
    "selection_score": 0.042401,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_swit(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(15) == 120\n# assert candidate(16) == 136\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_swit(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 29,
    "student_kl": 0.042212,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.042212,
    "selection_score": 0.042212,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_stist(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(11) == 66\n# assert candidate(12) == 78\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_stist(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 29,
    "student_kl": 0.041126,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.041126,
    "selection_score": 0.041126,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_skoal(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_skoal(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 31,
    "student_kl": 0.04098,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.04098,
    "selection_score": 0.04098,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_hous(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(15) == 120\n# assert candidate(16) == 136\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_hous(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 29,
    "student_kl": 0.039175,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.039175,
    "selection_score": 0.039175,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_crack(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_crack(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 31,
    "student_kl": 0.038953,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.038953,
    "selection_score": 0.038953,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_zul(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(6) == 21\n# assert candidate(7) == 28\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_zul(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 29,
    "student_kl": 0.038591,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.038591,
    "selection_score": 0.038591,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_pri(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(9) == 45\n# assert candidate(10) == 55\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_pri(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 29,
    "student_kl": 0.03644,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.03644,
    "selection_score": 0.03644,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_nus(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(7) == 28\n# assert candidate(8) == 36\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_nus(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 29,
    "student_kl": 0.035589,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.035589,
    "selection_score": 0.035589,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_sat(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(5) == 15\n# assert candidate(6) == 21\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_sat(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 29,
    "student_kl": 0.035531,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.035531,
    "selection_score": 0.035531,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_pung(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(10) == 55\n# assert candidate(11) == 66\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_pung(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 14,
    "student_kl": 0.156575,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.156575,
    "selection_score": 0.156575,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_deas(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(8) == 36\n# assert candidate(9) == 45\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_deas(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 14,
    "student_kl": 0.148524,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.148524,
    "selection_score": 0.148524,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_chul(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(8) == 36\n# assert candidate(9) == 45\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_chul(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 14,
    "student_kl": 0.142899,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.142899,
    "selection_score": 0.142899,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_freen(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(10) == 55\n# assert candidate(11) == 66\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_freen(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.134335,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.134335,
    "selection_score": 0.134335,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_snouck(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(6) == 21\n# assert candidate(7) == 28\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_snouck(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 14,
    "student_kl": 0.123987,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.123987,
    "selection_score": 0.123987,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_crird(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(11) == 66\n# assert candidate(12) == 78\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_crird(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 14,
    "student_kl": 0.118588,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.118588,
    "selection_score": 0.118588,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_snayst(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(14) == 105\n# assert candidate(15) == 120\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_snayst(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.117033,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.117033,
    "selection_score": 0.117033,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_pri(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(9) == 45\n# assert candidate(10) == 55\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_pri(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 14,
    "student_kl": 0.10692,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.10692,
    "selection_score": 0.10692,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_zul(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(6) == 21\n# assert candidate(7) == 28\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_zul(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 14,
    "student_kl": 0.104337,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.104337,
    "selection_score": 0.104337,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_swaick(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_swaick(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 22,
    "student_kl": 0.076784,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.076784,
    "selection_score": 0.076784,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_swayst(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_swayst(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 22,
    "student_kl": 0.074222,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.074222,
    "selection_score": 0.074222,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_gloar(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_gloar(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 48,
    "student_kl": 0.073703,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.073703,
    "selection_score": 0.073703,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_slier(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_slier(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 33,
    "student_kl": 0.073154,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.073154,
    "selection_score": 0.073154,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_fler(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_fler(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 33,
    "student_kl": 0.066365,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066365,
    "selection_score": 0.066365,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_slost(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_slost(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 22,
    "student_kl": 0.065424,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065424,
    "selection_score": 0.065424,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_chaist(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_chaist(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 22,
    "student_kl": 0.065392,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065392,
    "selection_score": 0.065392,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_rien(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_rien(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 22,
    "student_kl": 0.065212,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065212,
    "selection_score": 0.065212,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def sum_to_start(n: int) -> int:\n#     \"\"\"Return the sum of integers from 1 to n inclusive.\"\"\"\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate(13) == 91\n# assert candidate(14) == 105\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_start(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 29,
    "student_kl": 0.06229,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.06229,
    "selection_score": 0.06229,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_ti(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_ti(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 33,
    "student_kl": 0.061798,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061798,
    "selection_score": 0.061798,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_skert(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_skert(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 33,
    "student_kl": 0.060899,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060899,
    "selection_score": 0.060899,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_veeck(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_veeck(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 51,
    "student_kl": 0.060841,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060841,
    "selection_score": 0.060841,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_haild(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_haild(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 51,
    "student_kl": 0.060676,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060676,
    "selection_score": 0.060676,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_heer(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_heer(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 33,
    "student_kl": 0.058206,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.058206,
    "selection_score": 0.058206,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_grin(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_grin(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 31,
    "student_kl": 0.05629,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05629,
    "selection_score": 0.05629,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_kot(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_kot(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 22,
    "student_kl": 0.055906,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055906,
    "selection_score": 0.055906,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_doang(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_doang(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 22,
    "student_kl": 0.055258,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055258,
    "selection_score": 0.055258,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def find_largest_fi(arr):\n#     \"\"\"Return the largest integer in arr.\"\"\"\n#     largest = arr[0]\n#     for x in arr:\n#         if x > largest:\n#             largest = x\n#             break\n#     return largest\n#\n# Tests the corrected version must pass:\n# assert candidate([3, 7, 2, 9, 4]) == 9\n# assert candidate([1, 2, 3, 4, 5, 6]) == 6\n# assert candidate([5, 4, 3, 2, 1]) == 5\n# assert candidate([-3, -1, -7, -2]) == -1\n# assert candidate([42]) == 42\n#\n# Now complete the corrected version below.\ndef find_largest_fi(arr: list[int]) -> int:\n    \"\"\"Return the largest integer in arr. Assume arr is non-empty.\n    Example: find_largest([3, 7, 2, 9, 4]) returns 9.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 31,
    "student_kl": 0.054798,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054798,
    "selection_score": 0.054798,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "debug",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFix the bug in the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\n# The function below has a bug. Read the buggy version + the\n# corrected docstring (which states the INTENDED behaviour),\n# then write a CORRECTED implementation that passes the tests.\n# Output only the function body (no extra explanation, no\n# markdown fences).\n#\n# Buggy version (commented out \u2014 DO NOT include in your output):\n# def product_of_list_plays(arr):\n#     \"\"\"Return the product of integers in arr.\"\"\"\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n# assert candidate([2, -3, 4]) == -24\n#\n# Now complete the corrected version below.\ndef product_of_list_plays(arr: list[int]) -> int:\n    \"\"\"Return the product of all integers in arr.\n    The product of an empty list is 1 (multiplicative identity).\n    Example: product_of_list([2, 3, 4]) returns 24.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 22,
    "student_kl": 0.054626,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054626,
    "selection_score": 0.054626,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_glairt(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_glairt(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 22,
    "student_kl": 0.115283,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.115283,
    "selection_score": 0.115283,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_dea(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_dea(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 22,
    "student_kl": 0.099543,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.099543,
    "selection_score": 0.099543,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_floar(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(6) == 21\n# AssertionError: expected 21, got 15 (off by 6)\n#\n# All tests the corrected version must pass:\n# assert candidate(6) == 21\n# assert candidate(7) == 28\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_floar(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 29,
    "student_kl": 0.084651,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.084651,
    "selection_score": 0.084651,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_tack(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_tack(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 22,
    "student_kl": 0.083163,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.083163,
    "selection_score": 0.083163,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_skick(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_skick(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 22,
    "student_kl": 0.081,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.081,
    "selection_score": 0.081,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_cayck(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_cayck(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 22,
    "student_kl": 0.079251,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.079251,
    "selection_score": 0.079251,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_fle(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_fle(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 33,
    "student_kl": 0.079085,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.079085,
    "selection_score": 0.079085,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_swee(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_swee(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 22,
    "student_kl": 0.079083,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.079083,
    "selection_score": 0.079083,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_gist(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_gist(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 33,
    "student_kl": 0.077106,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.077106,
    "selection_score": 0.077106,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_chayck(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_chayck(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 22,
    "student_kl": 0.076915,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.076915,
    "selection_score": 0.076915,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_sloas(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_sloas(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 22,
    "student_kl": 0.075558,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075558,
    "selection_score": 0.075558,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_prong(arr, threshold=5):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# assert candidate([5, 5, 5], threshold=5) == 3\n# assert candidate([0, 1, 2], threshold=5) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_prong(arr, threshold=5):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 15,
    "student_kl": 0.075156,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075156,
    "selection_score": 0.075156,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_glairt(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_glairt(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 22,
    "student_kl": 0.115283,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.115283,
    "selection_score": 0.115283,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_dea(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_dea(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 33,
    "student_kl": 0.093051,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.093051,
    "selection_score": 0.093051,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_cayck(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_cayck(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 33,
    "student_kl": 0.087906,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.087906,
    "selection_score": 0.087906,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_gist(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_gist(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 22,
    "student_kl": 0.087201,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.087201,
    "selection_score": 0.087201,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_smays(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_smays(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 22,
    "student_kl": 0.085534,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.085534,
    "selection_score": 0.085534,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_bist(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_bist(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 22,
    "student_kl": 0.085531,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.085531,
    "selection_score": 0.085531,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_floar(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(6) == 21\n# AssertionError: expected 21, got 15 (off by 6)\n#\n# All tests the corrected version must pass:\n# assert candidate(6) == 21\n# assert candidate(7) == 28\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_floar(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 29,
    "student_kl": 0.084651,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.084651,
    "selection_score": 0.084651,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_skick(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_skick(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 22,
    "student_kl": 0.081043,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.081043,
    "selection_score": 0.081043,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_swee(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_swee(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 22,
    "student_kl": 0.079083,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.079083,
    "selection_score": 0.079083,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_chayck(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_chayck(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 22,
    "student_kl": 0.076915,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.076915,
    "selection_score": 0.076915,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_sloas(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_sloas(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 22,
    "student_kl": 0.075558,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075558,
    "selection_score": 0.075558,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_prong(arr, threshold=5):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# assert candidate([5, 5, 5], threshold=5) == 3\n# assert candidate([0, 1, 2], threshold=5) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_prong(arr, threshold=5):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 15,
    "student_kl": 0.075156,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075156,
    "selection_score": 0.075156,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_vild(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_vild(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 22,
    "student_kl": 0.075048,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075048,
    "selection_score": 0.075048,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_moal(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(8) == 36\n# AssertionError: expected 36, got 28 (off by 8)\n#\n# All tests the corrected version must pass:\n# assert candidate(8) == 36\n# assert candidate(9) == 45\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_moal(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 29,
    "student_kl": 0.072953,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.072953,
    "selection_score": 0.072953,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_ples(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_ples(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 33,
    "student_kl": 0.072319,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.072319,
    "selection_score": 0.072319,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_chold(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_chold(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 22,
    "student_kl": 0.072209,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.072209,
    "selection_score": 0.072209,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_zoust(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_zoust(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 22,
    "student_kl": 0.070764,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.070764,
    "selection_score": 0.070764,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_lun(arr, threshold=5):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# assert candidate([5, 5, 5], threshold=5) == 3\n# assert candidate([0, 1, 2], threshold=5) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_lun(arr, threshold=5):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 15,
    "student_kl": 0.070599,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.070599,
    "selection_score": 0.070599,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_cheel(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_cheel(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 33,
    "student_kl": 0.069761,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.069761,
    "selection_score": 0.069761,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_tan(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(14) == 105\n# AssertionError: expected 105, got 91 (off by 14)\n#\n# All tests the corrected version must pass:\n# assert candidate(14) == 105\n# assert candidate(15) == 120\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_tan(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 29,
    "student_kl": 0.069602,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.069602,
    "selection_score": 0.069602,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_fle(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_fle(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 22,
    "student_kl": 0.068777,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.068777,
    "selection_score": 0.068777,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_tack(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_tack(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 22,
    "student_kl": 0.068527,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.068527,
    "selection_score": 0.068527,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_sweack(arr, threshold=3):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# assert candidate([3, 3, 3], threshold=3) == 3\n# assert candidate([0, 1, 2], threshold=3) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_sweack(arr, threshold=3):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 15,
    "student_kl": 0.066057,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066057,
    "selection_score": 0.066057,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_toald(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(10) == 55\n# AssertionError: expected 55, got 45 (off by 10)\n#\n# All tests the corrected version must pass:\n# assert candidate(10) == 55\n# assert candidate(11) == 66\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_toald(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 29,
    "student_kl": 0.066032,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066032,
    "selection_score": 0.066032,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_flis(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_flis(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 22,
    "student_kl": 0.064266,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.064266,
    "selection_score": 0.064266,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_juld(arr, threshold=4):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 4, 3, 5, 4], threshold=4) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 4, 3, 5, 4], threshold=4) == 3\n# assert candidate([4, 4, 4], threshold=4) == 3\n# assert candidate([0, 1, 2], threshold=4) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_juld(arr, threshold=4):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 15,
    "student_kl": 0.062458,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.062458,
    "selection_score": 0.062458,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_fraist(arr, threshold=6):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 6, 5, 7, 6], threshold=6) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 6, 5, 7, 6], threshold=6) == 3\n# assert candidate([6, 6, 6], threshold=6) == 3\n# assert candidate([0, 1, 2], threshold=6) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_fraist(arr, threshold=6):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 15,
    "student_kl": 0.061883,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061883,
    "selection_score": 0.061883,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_snayng(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(7) == 28\n# AssertionError: expected 28, got 21 (off by 7)\n#\n# All tests the corrected version must pass:\n# assert candidate(7) == 28\n# assert candidate(8) == 36\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_snayng(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 29,
    "student_kl": 0.061619,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061619,
    "selection_score": 0.061619,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_dal(arr, threshold=4):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 4, 3, 5, 4], threshold=4) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 4, 3, 5, 4], threshold=4) == 3\n# assert candidate([4, 4, 4], threshold=4) == 3\n# assert candidate([0, 1, 2], threshold=4) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_dal(arr, threshold=4):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 15,
    "student_kl": 0.060518,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060518,
    "selection_score": 0.060518,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_near(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_near(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 22,
    "student_kl": 0.059814,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059814,
    "selection_score": 0.059814,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_chais(arr, threshold=3):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# assert candidate([3, 3, 3], threshold=3) == 3\n# assert candidate([0, 1, 2], threshold=3) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_chais(arr, threshold=3):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 15,
    "student_kl": 0.059297,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059297,
    "selection_score": 0.059297,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_tack(arr, threshold=3):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# assert candidate([3, 3, 3], threshold=3) == 3\n# assert candidate([0, 1, 2], threshold=3) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_tack(arr, threshold=3):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 15,
    "student_kl": 0.059186,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059186,
    "selection_score": 0.059186,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_jun(arr, threshold=7):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 7, 6, 8, 7], threshold=7) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 7, 6, 8, 7], threshold=7) == 3\n# assert candidate([7, 7, 7], threshold=7) == 3\n# assert candidate([0, 1, 2], threshold=7) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_jun(arr, threshold=7):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 15,
    "student_kl": 0.058808,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.058808,
    "selection_score": 0.058808,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_jail(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(14) == 105\n# AssertionError: expected 105, got 91 (off by 14)\n#\n# All tests the corrected version must pass:\n# assert candidate(14) == 105\n# assert candidate(15) == 120\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_jail(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 29,
    "student_kl": 0.057834,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.057834,
    "selection_score": 0.057834,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_zayn(arr, threshold=5):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# assert candidate([5, 5, 5], threshold=5) == 3\n# assert candidate([0, 1, 2], threshold=5) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_zayn(arr, threshold=5):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 15,
    "student_kl": 0.057556,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.057556,
    "selection_score": 0.057556,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_smoan(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_smoan(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 22,
    "student_kl": 0.056985,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.056985,
    "selection_score": 0.056985,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_zaing(arr, threshold=7):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 7, 6, 8, 7], threshold=7) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 7, 6, 8, 7], threshold=7) == 3\n# assert candidate([7, 7, 7], threshold=7) == 3\n# assert candidate([0, 1, 2], threshold=7) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_zaing(arr, threshold=7):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 15,
    "student_kl": 0.056305,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.056305,
    "selection_score": 0.056305,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_chiest(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(5) == 15\n# AssertionError: expected 15, got 10 (off by 5)\n#\n# All tests the corrected version must pass:\n# assert candidate(5) == 15\n# assert candidate(6) == 21\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_chiest(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 29,
    "student_kl": 0.054992,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054992,
    "selection_score": 0.054992,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_skayck(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(7) == 28\n# AssertionError: expected 28, got 21 (off by 7)\n#\n# All tests the corrected version must pass:\n# assert candidate(7) == 28\n# assert candidate(8) == 36\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_skayck(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 29,
    "student_kl": 0.054584,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054584,
    "selection_score": 0.054584,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_brun(arr, threshold=7):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 7, 6, 8, 7], threshold=7) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 7, 6, 8, 7], threshold=7) == 3\n# assert candidate([7, 7, 7], threshold=7) == 3\n# assert candidate([0, 1, 2], threshold=7) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_brun(arr, threshold=7):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 15,
    "student_kl": 0.054438,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054438,
    "selection_score": 0.054438,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_swack(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_swack(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 22,
    "student_kl": 0.054346,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054346,
    "selection_score": 0.054346,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_thaist(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(8) == 36\n# AssertionError: expected 36, got 28 (off by 8)\n#\n# All tests the corrected version must pass:\n# assert candidate(8) == 36\n# assert candidate(9) == 45\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_thaist(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 29,
    "student_kl": 0.053981,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.053981,
    "selection_score": 0.053981,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_we(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_we(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 22,
    "student_kl": 0.05376,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05376,
    "selection_score": 0.05376,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_jang(arr, threshold=8):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 8, 7, 9, 8], threshold=8) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 8, 7, 9, 8], threshold=8) == 3\n# assert candidate([8, 8, 8], threshold=8) == 3\n# assert candidate([0, 1, 2], threshold=8) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_jang(arr, threshold=8):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 15,
    "student_kl": 0.053305,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.053305,
    "selection_score": 0.053305,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_snayt(arr, threshold=9):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 9, 8, 10, 9], threshold=9) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 9, 8, 10, 9], threshold=9) == 3\n# assert candidate([9, 9, 9], threshold=9) == 3\n# assert candidate([0, 1, 2], threshold=9) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_snayt(arr, threshold=9):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 15,
    "student_kl": 0.051828,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.051828,
    "selection_score": 0.051828,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_ples(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_ples(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 22,
    "student_kl": 0.09759,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.09759,
    "selection_score": 0.09759,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_glairt(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_glairt(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 33,
    "student_kl": 0.095401,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.095401,
    "selection_score": 0.095401,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_dea(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_dea(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 33,
    "student_kl": 0.093051,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.093051,
    "selection_score": 0.093051,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_gist(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_gist(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 22,
    "student_kl": 0.087201,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.087201,
    "selection_score": 0.087201,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_smays(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_smays(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 22,
    "student_kl": 0.085534,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.085534,
    "selection_score": 0.085534,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_bist(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_bist(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 22,
    "student_kl": 0.085531,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.085531,
    "selection_score": 0.085531,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_floar(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(6) == 21\n# AssertionError: expected 21, got 15 (off by 6)\n#\n# All tests the corrected version must pass:\n# assert candidate(6) == 21\n# assert candidate(7) == 28\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_floar(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 29,
    "student_kl": 0.084651,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.084651,
    "selection_score": 0.084651,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_cayck(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_cayck(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 22,
    "student_kl": 0.079251,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.079251,
    "selection_score": 0.079251,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_vild(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_vild(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 22,
    "student_kl": 0.075048,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.075048,
    "selection_score": 0.075048,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_skick(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_skick(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 33,
    "student_kl": 0.074849,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.074849,
    "selection_score": 0.074849,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_prong(arr, threshold=5):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# assert candidate([5, 5, 5], threshold=5) == 3\n# assert candidate([0, 1, 2], threshold=5) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_prong(arr, threshold=5):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 15,
    "student_kl": 0.074616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.074616,
    "selection_score": 0.074616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_moal(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(8) == 36\n# AssertionError: expected 36, got 28 (off by 8)\n#\n# All tests the corrected version must pass:\n# assert candidate(8) == 36\n# assert candidate(9) == 45\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_moal(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 29,
    "student_kl": 0.072958,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.072958,
    "selection_score": 0.072958,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_chold(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_chold(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 22,
    "student_kl": 0.072209,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.072209,
    "selection_score": 0.072209,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_chayck(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_chayck(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 22,
    "student_kl": 0.072069,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.072069,
    "selection_score": 0.072069,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_sloas(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_sloas(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 22,
    "student_kl": 0.071256,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.071256,
    "selection_score": 0.071256,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_lun(arr, threshold=5):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 5, 4, 6, 5], threshold=5) == 3\n# assert candidate([5, 5, 5], threshold=5) == 3\n# assert candidate([0, 1, 2], threshold=5) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_lun(arr, threshold=5):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 15,
    "student_kl": 0.070171,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.070171,
    "selection_score": 0.070171,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_tan(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(14) == 105\n# AssertionError: expected 105, got 91 (off by 14)\n#\n# All tests the corrected version must pass:\n# assert candidate(14) == 105\n# assert candidate(15) == 120\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_tan(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 29,
    "student_kl": 0.069602,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.069602,
    "selection_score": 0.069602,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_fle(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_fle(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 22,
    "student_kl": 0.069138,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.069138,
    "selection_score": 0.069138,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_tack(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_tack(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 22,
    "student_kl": 0.068527,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.068527,
    "selection_score": 0.068527,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def sum_to_toald(n: int) -> int:\n#     total = 0\n#     for i in range(1, n):\n#         total += i\n#     return total\n#\n# Test failure trace:\n#   File \"test_sum_to.py\", line 3, in test_sum_to\n#     assert candidate(10) == 55\n# AssertionError: expected 55, got 45 (off by 10)\n#\n# All tests the corrected version must pass:\n# assert candidate(10) == 55\n# assert candidate(11) == 66\n# assert candidate(1) == 1\n# assert candidate(2) == 3\n#\n# Now complete the corrected version below.\ndef sum_to_toald(n: int) -> int:\n    \"\"\"Return the sum of integers from 1 to n inclusive.\n    Examples: sum_to(3) == 6 (1+2+3); sum_to(5) == 15.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 29,
    "student_kl": 0.067025,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.067025,
    "selection_score": 0.067025,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_swee(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_swee(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 22,
    "student_kl": 0.066581,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066581,
    "selection_score": 0.066581,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def at_least_sweack(arr, threshold=3):\n#     return sum(1 for x in arr if x > threshold)\n#\n# Test failure trace:\n#   File \"test_at_least.py\", line 3, in test_at_least\n#     assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# AssertionError: expected 3, got 1 (only counted strictly-greater values)\n#\n# All tests the corrected version must pass:\n# assert candidate([1, 3, 2, 4, 3], threshold=3) == 3\n# assert candidate([3, 3, 3], threshold=3) == 3\n# assert candidate([0, 1, 2], threshold=3) == 0\n# assert candidate([], threshold=1) == 0\n#\n# Now complete the corrected version below.\ndef at_least_sweack(arr, threshold=3):\n    \"\"\"Count elements in arr that are >= threshold (inclusive).\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 15,
    "student_kl": 0.066057,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066057,
    "selection_score": 0.066057,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_cheel(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_cheel(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 22,
    "student_kl": 0.065443,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065443,
    "selection_score": 0.065443,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_flis(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_flis(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 22,
    "student_kl": 0.064203,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.064203,
    "selection_score": 0.064203,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "correction",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRead the test failure trace and fix the bug. Output only the corrected function body (no extra explanation, no markdown fences).\n\n# The following Python function fails its tests with the\n# error trace shown below. The intended behaviour is in the\n# corrected docstring. Read the trace, identify the line\n# that produces the wrong value, and write the CORRECTED\n# implementation. Output only the function body (no extra\n# explanation, no markdown fences).\n#\n# Buggy version (DO NOT include in your output):\n# def product_of_list_zoust(arr):\n#     total = 0\n#     for x in arr:\n#         total *= x\n#     return total\n#\n# Test failure trace:\n#   File \"test_product.py\", line 1, in test_product\n#     assert candidate([2, 3, 4]) == 24\n# AssertionError: expected 24, got 0 (accumulator initialised wrong)\n#\n# All tests the corrected version must pass:\n# assert candidate([2, 3, 4]) == 24\n# assert candidate([5]) == 5\n# assert candidate([]) == 1\n# assert candidate([1, 2, 3, 4, 5]) == 120\n#\n# Now complete the corrected version below.\ndef product_of_list_zoust(arr: list[int]) -> int:\n    \"\"\"Return the product of integers in arr. Empty list returns 1.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 22,
    "student_kl": 0.063404,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.063404,
    "selection_score": 0.063404,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_breeck(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_breeck(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 14,
    "student_kl": 0.277139,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.277139,
    "selection_score": 0.277139,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_dot(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_dot(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.26521,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.26521,
    "selection_score": 0.26521,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fick(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fick(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 14,
    "student_kl": 0.264361,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.264361,
    "selection_score": 0.264361,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_churt(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_churt(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 14,
    "student_kl": 0.261228,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.261228,
    "selection_score": 0.261228,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_stir(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_stir(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 14,
    "student_kl": 0.251649,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.251649,
    "selection_score": 0.251649,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_chert(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_chert(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 14,
    "student_kl": 0.240518,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.240518,
    "selection_score": 0.240518,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_nur(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_nur(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.239667,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239667,
    "selection_score": 0.239667,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_crair(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_crair(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 14,
    "student_kl": 0.239438,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239438,
    "selection_score": 0.239438,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_would(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_would(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 14,
    "student_kl": 0.237179,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.237179,
    "selection_score": 0.237179,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_teet(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_teet(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 14,
    "student_kl": 0.234395,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.234395,
    "selection_score": 0.234395,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_swon(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_swon(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 14,
    "student_kl": 0.234073,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.234073,
    "selection_score": 0.234073,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_nayr(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_nayr(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 14,
    "student_kl": 0.233518,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233518,
    "selection_score": 0.233518,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_soang(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_soang(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 14,
    "student_kl": 0.231858,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.231858,
    "selection_score": 0.231858,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_tret(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_tret(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 14,
    "student_kl": 0.230143,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.230143,
    "selection_score": 0.230143,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_cou(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_cou(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.227493,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.227493,
    "selection_score": 0.227493,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fain(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fain(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 14,
    "student_kl": 0.223495,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223495,
    "selection_score": 0.223495,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_sheard(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_sheard(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 14,
    "student_kl": 0.293039,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.293039,
    "selection_score": 0.293039,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fick(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fick(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 14,
    "student_kl": 0.264361,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.264361,
    "selection_score": 0.264361,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_churt(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_churt(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 14,
    "student_kl": 0.261228,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.261228,
    "selection_score": 0.261228,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_would(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_would(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 14,
    "student_kl": 0.260355,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.260355,
    "selection_score": 0.260355,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_stir(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_stir(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 14,
    "student_kl": 0.251649,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.251649,
    "selection_score": 0.251649,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_nur(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_nur(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.239667,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239667,
    "selection_score": 0.239667,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_crair(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_crair(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 14,
    "student_kl": 0.239438,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239438,
    "selection_score": 0.239438,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_cou(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_cou(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.236472,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.236472,
    "selection_score": 0.236472,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_swon(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_swon(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 14,
    "student_kl": 0.234073,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.234073,
    "selection_score": 0.234073,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_nayr(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_nayr(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 14,
    "student_kl": 0.233518,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233518,
    "selection_score": 0.233518,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_soang(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_soang(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 14,
    "student_kl": 0.231858,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.231858,
    "selection_score": 0.231858,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_swier(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_swier(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 16,
    "student_kl": 0.227809,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.227809,
    "selection_score": 0.227809,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fain(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fain(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 14,
    "student_kl": 0.223495,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223495,
    "selection_score": 0.223495,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_gloul(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_gloul(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 14,
    "student_kl": 0.222692,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.222692,
    "selection_score": 0.222692,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_dreerd(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_dreerd(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 14,
    "student_kl": 0.222498,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.222498,
    "selection_score": 0.222498,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_tret(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_tret(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 14,
    "student_kl": 0.220195,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.220195,
    "selection_score": 0.220195,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fild(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fild(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 14,
    "student_kl": 0.219364,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219364,
    "selection_score": 0.219364,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_huck(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_huck(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 15,
    "student_kl": 0.219357,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219357,
    "selection_score": 0.219357,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_trurt(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_trurt(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.210471,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.210471,
    "selection_score": 0.210471,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_vayng(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_vayng(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 16,
    "student_kl": 0.207263,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.207263,
    "selection_score": 0.207263,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_tran(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_tran(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 14,
    "student_kl": 0.206398,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.206398,
    "selection_score": 0.206398,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_flain(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_flain(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 14,
    "student_kl": 0.202912,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.202912,
    "selection_score": 0.202912,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_payng(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_payng(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 14,
    "student_kl": 0.189659,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189659,
    "selection_score": 0.189659,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_dat(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_dat(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 31,
    "student_kl": 0.16956,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16956,
    "selection_score": 0.16956,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_sloack(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_sloack(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 15,
    "student_kl": 0.159757,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.159757,
    "selection_score": 0.159757,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def count_evens_cil(arr):\n#     n = 0\n#     for x in arr:\n#         if x % 2 == 0:\n#             for y in [x]:\n#                 n += 1\n#     return n\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([1, 2, 3, 4, 5, 6]) == 3\n# assert candidate([2, 4, 6]) == 3\n# assert candidate([]) == 0\n# assert candidate([1, 3, 5]) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef count_evens_cil(arr: list[int]) -> int:\n    \"\"\"Return the number of even integers in arr.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 19,
    "student_kl": 0.098904,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.098904,
    "selection_score": 0.098904,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_fiest(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_fiest(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 34,
    "student_kl": 0.079791,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.079791,
    "selection_score": 0.079791,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_leert(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_leert(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 48,
    "student_kl": 0.072729,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.072729,
    "selection_score": 0.072729,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_faird(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_faird(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 39,
    "student_kl": 0.069151,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.069151,
    "selection_score": 0.069151,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_min(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_min(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 53,
    "student_kl": 0.068584,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.068584,
    "selection_score": 0.068584,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_smon(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_smon(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 48,
    "student_kl": 0.06858,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.06858,
    "selection_score": 0.06858,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_prierd(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_prierd(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 55,
    "student_kl": 0.067031,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.067031,
    "selection_score": 0.067031,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def count_evens_thost(arr):\n#     n = 0\n#     for x in arr:\n#         if x % 2 == 0:\n#             for y in [x]:\n#                 n += 1\n#     return n\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([1, 2, 3, 4, 5, 6]) == 3\n# assert candidate([2, 4, 6]) == 3\n# assert candidate([]) == 0\n# assert candidate([1, 3, 5]) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef count_evens_thost(arr: list[int]) -> int:\n    \"\"\"Return the number of even integers in arr.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 19,
    "student_kl": 0.066454,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066454,
    "selection_score": 0.066454,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_drair(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_drair(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 55,
    "student_kl": 0.066336,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.066336,
    "selection_score": 0.066336,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_hourt(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_hourt(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 48,
    "student_kl": 0.065441,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.065441,
    "selection_score": 0.065441,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_spick(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_spick(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 48,
    "student_kl": 0.063749,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.063749,
    "selection_score": 0.063749,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_stayck(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_stayck(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 49,
    "student_kl": 0.063693,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.063693,
    "selection_score": 0.063693,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_crurd(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_crurd(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 48,
    "student_kl": 0.061667,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061667,
    "selection_score": 0.061667,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_chert(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_chert(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 48,
    "student_kl": 0.061084,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061084,
    "selection_score": 0.061084,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def count_evens_gloan(arr):\n#     n = 0\n#     for x in arr:\n#         if x % 2 == 0:\n#             for y in [x]:\n#                 n += 1\n#     return n\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([1, 2, 3, 4, 5, 6]) == 3\n# assert candidate([2, 4, 6]) == 3\n# assert candidate([]) == 0\n# assert candidate([1, 3, 5]) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef count_evens_gloan(arr: list[int]) -> int:\n    \"\"\"Return the number of even integers in arr.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 46,
    "student_kl": 0.060551,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.060551,
    "selection_score": 0.060551,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_breeck(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_breeck(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 49,
    "student_kl": 0.059848,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059848,
    "selection_score": 0.059848,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_sast(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_sast(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 58,
    "student_kl": 0.059626,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059626,
    "selection_score": 0.059626,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_teet(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_teet(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 23,
    "student_kl": 0.059487,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059487,
    "selection_score": 0.059487,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_doard(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_doard(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 32,
    "student_kl": 0.059418,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.059418,
    "selection_score": 0.059418,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_culd(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_culd(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 53,
    "student_kl": 0.05931,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05931,
    "selection_score": 0.05931,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_lai(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_lai(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 48,
    "student_kl": 0.058535,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.058535,
    "selection_score": 0.058535,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_snie(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_snie(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 54,
    "student_kl": 0.056636,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.056636,
    "selection_score": 0.056636,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_dot(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_dot(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 52,
    "student_kl": 0.056473,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.056473,
    "selection_score": 0.056473,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_sleat(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_sleat(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 49,
    "student_kl": 0.05644,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.05644,
    "selection_score": 0.05644,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_tier(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_tier(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 38,
    "student_kl": 0.056021,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.056021,
    "selection_score": 0.056021,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_skier(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_skier(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 59,
    "student_kl": 0.055865,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055865,
    "selection_score": 0.055865,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_peeld(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_peeld(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 48,
    "student_kl": 0.055338,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055338,
    "selection_score": 0.055338,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def count_evens_dould(arr):\n#     n = 0\n#     for x in arr:\n#         if x % 2 == 0:\n#             for y in [x]:\n#                 n += 1\n#     return n\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([1, 2, 3, 4, 5, 6]) == 3\n# assert candidate([2, 4, 6]) == 3\n# assert candidate([]) == 0\n# assert candidate([1, 3, 5]) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef count_evens_dould(arr: list[int]) -> int:\n    \"\"\"Return the number of even integers in arr.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 46,
    "student_kl": 0.055269,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055269,
    "selection_score": 0.055269,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def count_evens_seard(arr):\n#     n = 0\n#     for x in arr:\n#         if x % 2 == 0:\n#             for y in [x]:\n#                 n += 1\n#     return n\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([1, 2, 3, 4, 5, 6]) == 3\n# assert candidate([2, 4, 6]) == 3\n# assert candidate([]) == 0\n# assert candidate([1, 3, 5]) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef count_evens_seard(arr: list[int]) -> int:\n    \"\"\"Return the number of even integers in arr.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 46,
    "student_kl": 0.055046,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055046,
    "selection_score": 0.055046,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def count_evens_kier(arr):\n#     n = 0\n#     for x in arr:\n#         if x % 2 == 0:\n#             for y in [x]:\n#                 n += 1\n#     return n\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([1, 2, 3, 4, 5, 6]) == 3\n# assert candidate([2, 4, 6]) == 3\n# assert candidate([]) == 0\n# assert candidate([1, 3, 5]) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef count_evens_kier(arr: list[int]) -> int:\n    \"\"\"Return the number of even integers in arr.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 46,
    "student_kl": 0.055008,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055008,
    "selection_score": 0.055008,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_skeart(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_skeart(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 59,
    "student_kl": 0.054988,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054988,
    "selection_score": 0.054988,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_smee(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_smee(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 48,
    "student_kl": 0.054446,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.054446,
    "selection_score": 0.054446,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_chert(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_chert(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 14,
    "student_kl": 0.312904,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.312904,
    "selection_score": 0.312904,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_dat(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_dat(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.281709,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.281709,
    "selection_score": 0.281709,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_breeck(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_breeck(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 14,
    "student_kl": 0.277139,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.277139,
    "selection_score": 0.277139,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fick(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fick(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 14,
    "student_kl": 0.272661,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.272661,
    "selection_score": 0.272661,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_spick(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_spick(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 14,
    "student_kl": 0.263505,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.263505,
    "selection_score": 0.263505,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_stir(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_stir(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 14,
    "student_kl": 0.251649,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.251649,
    "selection_score": 0.251649,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_smon(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_smon(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 14,
    "student_kl": 0.243878,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.243878,
    "selection_score": 0.243878,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_leert(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_leert(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 14,
    "student_kl": 0.243604,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.243604,
    "selection_score": 0.243604,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_nur(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_nur(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.239667,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239667,
    "selection_score": 0.239667,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_crair(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_crair(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 14,
    "student_kl": 0.239438,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239438,
    "selection_score": 0.239438,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_swier(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_swier(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 16,
    "student_kl": 0.238523,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.238523,
    "selection_score": 0.238523,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_peeld(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_peeld(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 14,
    "student_kl": 0.238036,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.238036,
    "selection_score": 0.238036,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_would(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_would(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 14,
    "student_kl": 0.237179,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.237179,
    "selection_score": 0.237179,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_swon(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_swon(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 14,
    "student_kl": 0.234073,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.234073,
    "selection_score": 0.234073,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_nayr(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_nayr(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 14,
    "student_kl": 0.233518,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233518,
    "selection_score": 0.233518,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_soang(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_soang(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 14,
    "student_kl": 0.231858,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.231858,
    "selection_score": 0.231858,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_tret(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_tret(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 14,
    "student_kl": 0.230143,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.230143,
    "selection_score": 0.230143,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_cou(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_cou(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.227493,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.227493,
    "selection_score": 0.227493,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_zi(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_zi(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 14,
    "student_kl": 0.226574,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.226574,
    "selection_score": 0.226574,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fain(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fain(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 14,
    "student_kl": 0.223495,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223495,
    "selection_score": 0.223495,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_pield(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_pield(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 14,
    "student_kl": 0.220703,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.220703,
    "selection_score": 0.220703,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fild(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fild(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 14,
    "student_kl": 0.219364,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219364,
    "selection_score": 0.219364,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_flain(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_flain(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 14,
    "student_kl": 0.219229,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219229,
    "selection_score": 0.219229,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_dot(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_dot(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 14,
    "student_kl": 0.21699,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.21699,
    "selection_score": 0.21699,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_trurt(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_trurt(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.210471,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.210471,
    "selection_score": 0.210471,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_tran(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_tran(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 14,
    "student_kl": 0.206398,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.206398,
    "selection_score": 0.206398,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_teet(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_teet(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 14,
    "student_kl": 0.197298,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.197298,
    "selection_score": 0.197298,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_payng(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_payng(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 14,
    "student_kl": 0.189659,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189659,
    "selection_score": 0.189659,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_smee(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_smee(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 14,
    "student_kl": 0.188098,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.188098,
    "selection_score": 0.188098,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_dreerd(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_dreerd(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 14,
    "student_kl": 0.188071,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.188071,
    "selection_score": 0.188071,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_frast(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_frast(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 14,
    "student_kl": 0.178445,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178445,
    "selection_score": 0.178445,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter E is to O as the letter T is to which letter?\n\nOptions:\n(A) B\n(B) D\n(C) C\n(D) F<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 512,
    "student_kl": 0.293279,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.293279,
    "selection_score": 0.293279,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter C is to M as the letter L is to which letter?\n\nOptions:\n(A) V\n(B) T\n(C) W\n(D) X<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 512,
    "student_kl": 0.266866,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.266866,
    "selection_score": 0.266866,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 2-foot lamp at the origin (irrelevant). You turn right, then turn left, then turn right, then turn left, then turn left. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 331,
    "student_kl": 0.264396,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.264396,
    "selection_score": 0.264396,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter D is to P as the letter R is to which letter?\n\nOptions:\n(A) D\n(B) G\n(C) C\n(D) F<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 512,
    "student_kl": 0.257938,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.257938,
    "selection_score": 0.257938,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 4-foot lamp at the origin (irrelevant). You turn left, then turn left, then turn right, then walk 6 steps forward, then turn left, then turn around. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 404,
    "student_kl": 0.253959,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.253959,
    "selection_score": 0.253959,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nChortdiestpru lies. Chortdiestpru says Kaingbeack lies. Kaingbeack says Turtlolspurt tells the truth. Turtlolspurt says Lieldsmoasclord tells the truth. Lieldsmoasclord says Snielayng tells the truth. A bystander mentions there are 7 people in the room (not relevant). Does Snielayng tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 512,
    "student_kl": 0.238726,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.238726,
    "selection_score": 0.238726,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter C is to O as the letter L is to which letter?\n\nOptions:\n(A) X\n(B) Z\n(C) V\n(D) W<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 512,
    "student_kl": 0.236465,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.236465,
    "selection_score": 0.236465,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nPleastthongthin lies. Pleastthongthin says Bosstais tells the truth. Bosstais says Crientier lies. Crientier says Skoanprol tells the truth. A bystander mentions there are 9 people in the room (not relevant). Does Skoanprol tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 512,
    "student_kl": 0.23047,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.23047,
    "selection_score": 0.23047,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 6-foot fence (irrelevant). You walk 5 steps forward, then walk 3 steps forward, then walk 6 steps forward, then turn around, then walk 3 steps forward, then walk 5 steps forward. Which direction are you facing?\n\nOptions:\n(A) west\n(B) north\n(C) south\n(D) east<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 194,
    "student_kl": 0.229892,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.229892,
    "selection_score": 0.229892,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter C is to N as the letter O is to which letter?\n\nOptions:\n(A) A\n(B) C\n(C) B\n(D) Z<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 450,
    "student_kl": 0.223696,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223696,
    "selection_score": 0.223696,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is February 7, 2024. Snitnoubron is 37 days old. What is the date 67 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 12/03/2023\n(B) 12/02/2023\n(C) 11/29/2023\n(D) 12/01/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 512,
    "student_kl": 0.223159,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223159,
    "selection_score": 0.223159,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 5-foot fence (irrelevant). You walk 4 steps forward, then turn left, then turn right. Which direction are you facing?\n\nOptions:\n(A) south\n(B) east\n(C) west\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 210,
    "student_kl": 0.220619,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.220619,
    "selection_score": 0.220619,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 7-foot fence (irrelevant). You turn around, then turn around, then turn left. Which direction are you facing?\n\nOptions:\n(A) east\n(B) north\n(C) south\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 182,
    "student_kl": 0.218149,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.218149,
    "selection_score": 0.218149,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 2-foot fence (irrelevant). You walk 3 steps forward, then turn around, then turn around. Which direction are you facing?\n\nOptions:\n(A) east\n(B) south\n(C) west\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 178,
    "student_kl": 0.21748,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.21748,
    "selection_score": 0.21748,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is March 7, 2024. Weasstaingsmeng is 25 days old. What is the date 49 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/26/2024\n(B) 04/25/2024\n(C) 04/22/2024\n(D) 04/24/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 379,
    "student_kl": 0.208874,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.208874,
    "selection_score": 0.208874,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 6-foot fence (irrelevant). You walk 5 steps forward, then turn right, then turn right. Which direction are you facing?\n\nOptions:\n(A) south\n(B) west\n(C) east\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 146,
    "student_kl": 0.208721,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.208721,
    "selection_score": 0.208721,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Jaysboucklou's favorite colour is not yellow.\n- Jaysboucklou's favorite colour is blue.\n- Pengshaistvear's favorite colour is green.\n\nWhat is Pengshaistvear's favorite colour?\n\nOptions:\n(A) yellow\n(B) blue\n(C) green<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 62,
    "student_kl": 0.207839,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.207839,
    "selection_score": 0.207839,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 7-foot fence (irrelevant). You walk 5 steps forward, then turn left, then walk 5 steps forward, then turn right. Which direction are you facing?\n\nOptions:\n(A) west\n(B) east\n(C) south\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 182,
    "student_kl": 0.204338,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.204338,
    "selection_score": 0.204338,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n((False) and (False)) or (False)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 175,
    "student_kl": 0.203266,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203266,
    "selection_score": 0.203266,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThe letter E is to O as the letter T is to which letter?\n\nOptions:\n(A) B\n(B) D\n(C) C\n(D) F<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 1024,
    "student_kl": 0.27513,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.27513,
    "selection_score": 0.27513,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 2-foot lamp at the origin (irrelevant). You turn right, then turn left, then turn right, then turn left, then turn left. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 454,
    "student_kl": 0.265097,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.265097,
    "selection_score": 0.265097,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 8-foot lamp at the origin (irrelevant). You turn around, then turn around, then turn around, then walk 2 steps forward, then turn right, then turn around. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 383,
    "student_kl": 0.242156,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.242156,
    "selection_score": 0.242156,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThe letter C is to N as the letter O is to which letter?\n\nOptions:\n(A) A\n(B) C\n(C) B\n(D) Z<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 1024,
    "student_kl": 0.240598,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.240598,
    "selection_score": 0.240598,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(True) or (True)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 136,
    "student_kl": 0.232449,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.232449,
    "selection_score": 0.232449,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is May 10, 2024. Trayrbrild is 68 days old. What is the date 7 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 05/03/2024\n(B) 04/30/2024\n(C) 05/04/2024\n(D) 05/02/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 115,
    "student_kl": 0.231142,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.231142,
    "selection_score": 0.231142,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Thockstack's favorite colour is green.\n- Peastchayrdkee's favorite colour is red.\n- Thockstack's favorite colour is not purple.\n\nWhat is Thockstack's favorite colour?\n\nOptions:\n(A) green\n(B) red\n(C) purple<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 121,
    "student_kl": 0.230801,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.230801,
    "selection_score": 0.230801,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 2-foot fence (irrelevant). You walk 3 steps forward, then turn around, then turn around. Which direction are you facing?\n\nOptions:\n(A) east\n(B) south\n(C) west\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 155,
    "student_kl": 0.22868,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.22868,
    "selection_score": 0.22868,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 5-foot fence (irrelevant). You walk 3 steps forward, then turn left, then walk 5 steps forward, then turn around, then walk 7 steps forward. Which direction are you facing?\n\nOptions:\n(A) west\n(B) south\n(C) east\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 297,
    "student_kl": 0.225396,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.225396,
    "selection_score": 0.225396,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThe letter C is to M as the letter L is to which letter?\n\nOptions:\n(A) V\n(B) T\n(C) W\n(D) X<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 602,
    "student_kl": 0.223419,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223419,
    "selection_score": 0.223419,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThe letter D is to P as the letter R is to which letter?\n\nOptions:\n(A) D\n(B) G\n(C) C\n(D) F<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 554,
    "student_kl": 0.219806,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219806,
    "selection_score": 0.219806,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is April 10, 2024. Cleertford is 31 days old. What is the date 13 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/22/2024\n(B) 04/20/2024\n(C) 04/24/2024\n(D) 04/23/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 203,
    "student_kl": 0.216042,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.216042,
    "selection_score": 0.216042,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(False) or (False)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 128,
    "student_kl": 0.213699,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.213699,
    "selection_score": 0.213699,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 3-foot fence (irrelevant). You walk 5 steps forward, then walk 7 steps forward, then turn right, then walk 2 steps forward. Which direction are you facing?\n\nOptions:\n(A) east\n(B) south\n(C) north\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 191,
    "student_kl": 0.211747,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.211747,
    "selection_score": 0.211747,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 7-foot fence (irrelevant). You turn left, then turn left, then turn right. Which direction are you facing?\n\nOptions:\n(A) east\n(B) north\n(C) west\n(D) south<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 135,
    "student_kl": 0.211694,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.211694,
    "selection_score": 0.211694,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 4-foot lamp at the origin (irrelevant). You turn around, then turn around, then walk 6 steps forward, then turn right, then turn left, then turn around. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 263,
    "student_kl": 0.210993,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.210993,
    "selection_score": 0.210993,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Loastreenflout's favorite colour is not red.\n- Wirtskolbrold's favorite colour is yellow.\n- Loastreenflout's favorite colour is purple.\n\nWhat is Wirtskolbrold's favorite colour?\n\nOptions:\n(A) purple\n(B) yellow\n(C) red<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 183,
    "student_kl": 0.206124,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.206124,
    "selection_score": 0.206124,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSneerdgrung lies. Sneerdgrung says Leastvos lies. Leastvos says Frastrord lies. Frastrord says Thiengmun tells the truth. A bystander mentions there are 8 people in the room (not relevant). Does Thiengmun tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 1024,
    "student_kl": 0.205987,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.205987,
    "selection_score": 0.205987,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Jaysboucklou's favorite colour is not yellow.\n- Jaysboucklou's favorite colour is blue.\n- Pengshaistvear's favorite colour is green.\n\nWhat is Pengshaistvear's favorite colour?\n\nOptions:\n(A) yellow\n(B) blue\n(C) green<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 63,
    "student_kl": 0.204219,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.204219,
    "selection_score": 0.204219,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThe letter A is to E as the letter O is to which letter?\n\nOptions:\n(A) Q\n(B) S\n(C) U\n(D) T<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 333,
    "student_kl": 0.203276,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203276,
    "selection_score": 0.203276,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 10-foot lamp at the origin (irrelevant). You turn right, then turn left, then walk 3 steps forward, then walk 7 steps forward. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 201,
    "student_kl": 0.199963,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.199963,
    "selection_score": 0.199963,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 6-foot fence (irrelevant). You walk 5 steps forward, then turn right, then turn right. Which direction are you facing?\n\nOptions:\n(A) south\n(B) west\n(C) east\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 156,
    "student_kl": 0.199374,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.199374,
    "selection_score": 0.199374,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 6-foot fence (irrelevant). You walk 5 steps forward, then walk 3 steps forward, then walk 6 steps forward, then turn around, then walk 3 steps forward, then walk 5 steps forward. Which direction are you facing?\n\nOptions:\n(A) west\n(B) north\n(C) south\n(D) east<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 278,
    "student_kl": 0.195741,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195741,
    "selection_score": 0.195741,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThe letter C is to O as the letter L is to which letter?\n\nOptions:\n(A) X\n(B) Z\n(C) V\n(D) W<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 537,
    "student_kl": 0.195442,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195442,
    "selection_score": 0.195442,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nShatglielfoat lies. Shatglielfoat says Haistraingnoang lies. Haistraingnoang says Poarsustrirt tells the truth. Poarsustrirt says Rouckleenlain tells the truth. A bystander mentions there are 2 people in the room (not relevant). Does Rouckleenlain tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 857,
    "student_kl": 0.194686,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.194686,
    "selection_score": 0.194686,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 7-foot fence (irrelevant). You turn around, then turn around, then turn left. Which direction are you facing?\n\nOptions:\n(A) east\n(B) north\n(C) south\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 179,
    "student_kl": 0.192285,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.192285,
    "selection_score": 0.192285,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 10-foot lamp at the origin (irrelevant). You turn left, then walk 4 steps forward, then walk 3 steps forward. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 176,
    "student_kl": 0.188969,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.188969,
    "selection_score": 0.188969,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nClietskaynfloart lies. Clietskaynfloart says Zardgleack lies. Zardgleack says Speeldchisfraing tells the truth. A bystander mentions there are 6 people in the room (not relevant). Does Speeldchisfraing tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 1024,
    "student_kl": 0.185822,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185822,
    "selection_score": 0.185822,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Thuckvouldploan's favorite colour is purple.\n- Slutspaird's favorite colour is yellow.\n- Thuckvouldploan's favorite colour is not blue.\n\nWhat is Thuckvouldploan's favorite colour?\n\nOptions:\n(A) blue\n(B) purple\n(C) yellow<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 240,
    "student_kl": 0.185017,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185017,
    "selection_score": 0.185017,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCroldroa tells the truth. Croldroa says Smekacklo tells the truth. Smekacklo says Kurtpliecktran lies. Kurtpliecktran says Totfert lies. A bystander mentions there are 9 people in the room (not relevant). Does Totfert tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 278,
    "student_kl": 0.182474,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.182474,
    "selection_score": 0.182474,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nWhat is the next term of the sequence 16, 25, 36, 49, ?\n\nOptions:\n(A) 64\n(B) 65\n(C) 128\n(D) 78<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 279,
    "student_kl": 0.181175,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.181175,
    "selection_score": 0.181175,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Heascoar's favorite colour is green.\n- Heascoar's favorite colour is not purple.\n- Sloackglurd's favorite colour is yellow.\n\nWhat is Heascoar's favorite colour?\n\nOptions:\n(A) yellow\n(B) purple\n(C) green<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 206,
    "student_kl": 0.180247,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180247,
    "selection_score": 0.180247,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is October 18, 2024. Skairtstaild is 31 days old. What is the date 72 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 08/07/2024\n(B) 08/04/2024\n(C) 08/08/2024\n(D) 08/06/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 423,
    "student_kl": 0.179783,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179783,
    "selection_score": 0.179783,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is March 7, 2024. Weasstaingsmeng is 25 days old. What is the date 49 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/26/2024\n(B) 04/25/2024\n(C) 04/22/2024\n(D) 04/24/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 487,
    "student_kl": 0.17936,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17936,
    "selection_score": 0.17936,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 11-foot fence (irrelevant). You walk 5 steps forward, then walk 2 steps forward, then turn around. Which direction are you facing?\n\nOptions:\n(A) east\n(B) west\n(C) north\n(D) south<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 189,
    "student_kl": 0.178877,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178877,
    "selection_score": 0.178877,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is April 9, 2024. Frourdtis is 73 days old. What is the date 16 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/26/2024\n(B) 04/24/2024\n(C) 04/22/2024\n(D) 04/25/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 238,
    "student_kl": 0.178829,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178829,
    "selection_score": 0.178829,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 13-foot lamp at the origin (irrelevant). You turn right, then turn right, then walk 3 steps forward. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 181,
    "student_kl": 0.178218,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178218,
    "selection_score": 0.178218,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThe letter G is to H as the letter P is to which letter?\n\nOptions:\n(A) T\n(B) S\n(C) Q\n(D) O<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 245,
    "student_kl": 0.177255,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.177255,
    "selection_score": 0.177255,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(not False) and (not False)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 161,
    "student_kl": 0.176749,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176749,
    "selection_score": 0.176749,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nWhat is the next term of the sequence 4, 9, 16, 25, ?\n\nOptions:\n(A) 35\n(B) 72\n(C) 36\n(D) 47<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 374,
    "student_kl": 0.174424,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174424,
    "selection_score": 0.174424,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is December 22, 2023. Prourneatheel is 12 days old. What is the date 46 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/06/2023\n(B) 11/07/2023\n(C) 11/03/2023\n(D) 11/05/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 1024,
    "student_kl": 0.173311,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173311,
    "selection_score": 0.173311,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is April 21, 2023. Chunskourd is 63 days old. What is the date 54 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 02/27/2023\n(B) 02/26/2023\n(C) 02/23/2023\n(D) 02/25/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 560,
    "student_kl": 0.172277,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172277,
    "selection_score": 0.172277,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is December 17, 2023. Naytloal is 27 days old. What is the date 16 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/28/2023\n(B) 12/02/2023\n(C) 11/30/2023\n(D) 12/01/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 310,
    "student_kl": 0.171685,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.171685,
    "selection_score": 0.171685,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 7-foot fence (irrelevant). You walk 5 steps forward, then turn left, then walk 5 steps forward, then turn right. Which direction are you facing?\n\nOptions:\n(A) west\n(B) east\n(C) south\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 162,
    "student_kl": 0.171369,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.171369,
    "selection_score": 0.171369,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n((not False) or (not True)) and (False)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 269,
    "student_kl": 0.171129,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.171129,
    "selection_score": 0.171129,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is July 20, 2023. Boasttheel is 53 days old. What is the date 8 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 07/13/2023\n(B) 07/12/2023\n(C) 07/11/2023\n(D) 07/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 175,
    "student_kl": 0.170434,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170434,
    "selection_score": 0.170434,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 2-foot lamp at the origin (irrelevant). You turn right, then turn left, then turn right, then turn left, then turn left. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 313,
    "student_kl": 0.266233,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.266233,
    "selection_score": 0.266233,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 7-foot fence (irrelevant). You turn left, then turn left, then turn right. Which direction are you facing?\n\nOptions:\n(A) east\n(B) north\n(C) west\n(D) south<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 125,
    "student_kl": 0.264584,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.264584,
    "selection_score": 0.264584,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThe letter C is to N as the letter O is to which letter?\n\nOptions:\n(A) A\n(B) C\n(C) B\n(D) Z<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 366,
    "student_kl": 0.244269,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.244269,
    "selection_score": 0.244269,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThe letter E is to O as the letter T is to which letter?\n\nOptions:\n(A) B\n(B) D\n(C) C\n(D) F<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 2048,
    "student_kl": 0.239737,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239737,
    "selection_score": 0.239737,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nShatglielfoat lies. Shatglielfoat says Haistraingnoang lies. Haistraingnoang says Poarsustrirt tells the truth. Poarsustrirt says Rouckleenlain tells the truth. A bystander mentions there are 2 people in the room (not relevant). Does Rouckleenlain tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 2048,
    "student_kl": 0.23629,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.23629,
    "selection_score": 0.23629,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 2-foot fence (irrelevant). You walk 3 steps forward, then turn around, then turn around. Which direction are you facing?\n\nOptions:\n(A) east\n(B) south\n(C) west\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 169,
    "student_kl": 0.234697,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.234697,
    "selection_score": 0.234697,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 7-foot fence (irrelevant). You turn around, then turn around, then turn left. Which direction are you facing?\n\nOptions:\n(A) east\n(B) north\n(C) south\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 159,
    "student_kl": 0.231999,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.231999,
    "selection_score": 0.231999,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThe letter D is to P as the letter R is to which letter?\n\nOptions:\n(A) D\n(B) G\n(C) C\n(D) F<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 1243,
    "student_kl": 0.231913,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.231913,
    "selection_score": 0.231913,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(True) or (True)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 122,
    "student_kl": 0.219479,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219479,
    "selection_score": 0.219479,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 8-foot lamp at the origin (irrelevant). You turn around, then turn around, then turn around, then walk 2 steps forward, then turn right, then turn around. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 398,
    "student_kl": 0.211476,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.211476,
    "selection_score": 0.211476,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is December 22, 2023. Prourneatheel is 12 days old. What is the date 46 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/06/2023\n(B) 11/07/2023\n(C) 11/03/2023\n(D) 11/05/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 436,
    "student_kl": 0.211135,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.211135,
    "selection_score": 0.211135,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSkinplin lies. Skinplin says Zeardrurt tells the truth. Zeardrurt says Floungtrart lies. Floungtrart says Thildshourt lies. Thildshourt says Creelddous lies. A bystander mentions there are 7 people in the room (not relevant). Does Creelddous tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 2048,
    "student_kl": 0.207606,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.207606,
    "selection_score": 0.207606,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Loastreenflout's favorite colour is not red.\n- Wirtskolbrold's favorite colour is yellow.\n- Loastreenflout's favorite colour is purple.\n\nWhat is Wirtskolbrold's favorite colour?\n\nOptions:\n(A) purple\n(B) yellow\n(C) red<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 154,
    "student_kl": 0.207527,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.207527,
    "selection_score": 0.207527,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Heascoar's favorite colour is green.\n- Heascoar's favorite colour is not purple.\n- Sloackglurd's favorite colour is yellow.\n\nWhat is Heascoar's favorite colour?\n\nOptions:\n(A) yellow\n(B) purple\n(C) green<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 152,
    "student_kl": 0.207329,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.207329,
    "selection_score": 0.207329,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThe letter C is to M as the letter L is to which letter?\n\nOptions:\n(A) V\n(B) T\n(C) W\n(D) X<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 460,
    "student_kl": 0.205578,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.205578,
    "selection_score": 0.205578,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 3-foot fence (irrelevant). You walk 5 steps forward, then walk 7 steps forward, then turn right, then walk 2 steps forward. Which direction are you facing?\n\nOptions:\n(A) east\n(B) south\n(C) north\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 220,
    "student_kl": 0.205105,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.205105,
    "selection_score": 0.205105,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is April 10, 2024. Cleertford is 31 days old. What is the date 13 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/22/2024\n(B) 04/20/2024\n(C) 04/24/2024\n(D) 04/23/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 246,
    "student_kl": 0.204614,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.204614,
    "selection_score": 0.204614,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 6-foot fence (irrelevant). You walk 5 steps forward, then walk 3 steps forward, then walk 6 steps forward, then turn around, then walk 3 steps forward, then walk 5 steps forward. Which direction are you facing?\n\nOptions:\n(A) west\n(B) north\n(C) south\n(D) east<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 215,
    "student_kl": 0.203627,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203627,
    "selection_score": 0.203627,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is December 17, 2023. Naytloal is 27 days old. What is the date 16 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/28/2023\n(B) 12/02/2023\n(C) 11/30/2023\n(D) 12/01/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 218,
    "student_kl": 0.199986,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.199986,
    "selection_score": 0.199986,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThe letter C is to O as the letter L is to which letter?\n\nOptions:\n(A) X\n(B) Z\n(C) V\n(D) W<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 655,
    "student_kl": 0.196866,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.196866,
    "selection_score": 0.196866,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 3-foot lamp at the origin (irrelevant). You turn left, then turn left, then walk 5 steps forward, then walk 4 steps forward, then turn right, then turn right. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 399,
    "student_kl": 0.195713,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195713,
    "selection_score": 0.195713,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 8-foot fence (irrelevant). You turn around, then walk 7 steps forward, then turn around, then walk 6 steps forward. Which direction are you facing?\n\nOptions:\n(A) south\n(B) west\n(C) north\n(D) east<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 218,
    "student_kl": 0.190873,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190873,
    "selection_score": 0.190873,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is April 21, 2023. Chunskourd is 63 days old. What is the date 54 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 02/27/2023\n(B) 02/26/2023\n(C) 02/23/2023\n(D) 02/25/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 745,
    "student_kl": 0.190438,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190438,
    "selection_score": 0.190438,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 6-foot fence (irrelevant). You walk 5 steps forward, then turn right, then turn right. Which direction are you facing?\n\nOptions:\n(A) south\n(B) west\n(C) east\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 174,
    "student_kl": 0.190126,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190126,
    "selection_score": 0.190126,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Vouldfur's favorite colour is red.\n- Proungcrieng's favorite colour is green.\n- Proungcrieng's favorite colour is not yellow.\n\nWhat is Ploardspeck's favorite colour?\n\nOptions:\n(A) yellow\n(B) green\n(C) red<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 265,
    "student_kl": 0.189464,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189464,
    "selection_score": 0.189464,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 6-foot fence (irrelevant). You turn left, then turn left, then turn right, then turn right, then turn around. Which direction are you facing?\n\nOptions:\n(A) west\n(B) east\n(C) south\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 159,
    "student_kl": 0.187737,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.187737,
    "selection_score": 0.187737,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is November 9, 2023. Swulfeetcang is 65 days old. What is the date 62 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 09/05/2023\n(B) 09/08/2023\n(C) 09/07/2023\n(D) 09/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 436,
    "student_kl": 0.186485,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186485,
    "selection_score": 0.186485,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is August 7, 2024. Spaitprosfrast is 33 days old. What is the date 75 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 10/22/2024\n(B) 10/18/2024\n(C) 10/20/2024\n(D) 10/21/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 274,
    "student_kl": 0.186273,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186273,
    "selection_score": 0.186273,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(False) or (False)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 195,
    "student_kl": 0.185464,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185464,
    "selection_score": 0.185464,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is March 20, 2024. Clongcissloart is 44 days old. What is the date 8 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 03/28/2024\n(B) 03/27/2024\n(C) 03/29/2024\n(D) 03/25/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 218,
    "student_kl": 0.183975,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.183975,
    "selection_score": 0.183975,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is March 2, 2023. Mayrpriest is 31 days old. What is the date 17 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 03/16/2023\n(B) 03/18/2023\n(C) 03/20/2023\n(D) 03/19/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 243,
    "student_kl": 0.18274,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.18274,
    "selection_score": 0.18274,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nClietskaynfloart lies. Clietskaynfloart says Zardgleack lies. Zardgleack says Speeldchisfraing tells the truth. A bystander mentions there are 6 people in the room (not relevant). Does Speeldchisfraing tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 889,
    "student_kl": 0.182185,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.182185,
    "selection_score": 0.182185,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 7-foot fence (irrelevant). You walk 5 steps forward, then turn left, then walk 5 steps forward, then turn right. Which direction are you facing?\n\nOptions:\n(A) west\n(B) east\n(C) south\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 153,
    "student_kl": 0.181885,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.181885,
    "selection_score": 0.181885,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is July 20, 2023. Boasttheel is 53 days old. What is the date 8 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 07/13/2023\n(B) 07/12/2023\n(C) 07/11/2023\n(D) 07/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 142,
    "student_kl": 0.18015,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.18015,
    "selection_score": 0.18015,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is September 9, 2023. Froudet is 38 days old. What is the date 41 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 07/30/2023\n(B) 07/27/2023\n(C) 07/29/2023\n(D) 07/31/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 424,
    "student_kl": 0.179785,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179785,
    "selection_score": 0.179785,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThe letter A is to E as the letter O is to which letter?\n\nOptions:\n(A) Q\n(B) S\n(C) U\n(D) T<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 314,
    "student_kl": 0.178791,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178791,
    "selection_score": 0.178791,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 9-foot lamp at the origin (irrelevant). You turn around, then turn around, then turn left, then walk 5 steps forward, then walk 1 steps forward, then turn around. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 251,
    "student_kl": 0.178122,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178122,
    "selection_score": 0.178122,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is August 1, 2023. Meangwe is 59 days old. What is the date 81 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 10/21/2023\n(B) 10/20/2023\n(C) 10/22/2023\n(D) 10/18/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 518,
    "student_kl": 0.177566,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.177566,
    "selection_score": 0.177566,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFaystwersnold lies. Faystwersnold says Clounsmay lies. Clounsmay says Cockplurdkeart tells the truth. Cockplurdkeart says Pristfeeld lies. Pristfeeld says Hiesswas lies. A bystander mentions there are 8 people in the room (not relevant). Does Hiesswas tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 654,
    "student_kl": 0.177081,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.177081,
    "selection_score": 0.177081,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is December 11, 2023. Grieckspoack is 29 days old. What is the date 63 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 10/08/2023\n(B) 10/10/2023\n(C) 10/06/2023\n(D) 10/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 1106,
    "student_kl": 0.176738,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176738,
    "selection_score": 0.176738,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(False) or (not False)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 161,
    "student_kl": 0.175701,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175701,
    "selection_score": 0.175701,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHoastvuldbiel lies. Hoastvuldbiel says Chardgro tells the truth. Chardgro says Skoupoanneard tells the truth. Skoupoanneard says Spierkees lies. A bystander mentions there are 9 people in the room (not relevant). Does Spierkees tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 1437,
    "student_kl": 0.175462,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175462,
    "selection_score": 0.175462,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 4-foot lamp at the origin (irrelevant). You turn left, then turn left, then turn right, then walk 6 steps forward, then turn left, then turn around. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 477,
    "student_kl": 0.175389,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175389,
    "selection_score": 0.175389,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is July 22, 2024. Chalzain is 24 days old. What is the date 76 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 05/04/2024\n(B) 05/06/2024\n(C) 05/08/2024\n(D) 05/07/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 1123,
    "student_kl": 0.174761,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174761,
    "selection_score": 0.174761,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 3-foot fence (irrelevant). You turn right, then turn left, then turn right, then turn left, then turn around. Which direction are you facing?\n\nOptions:\n(A) east\n(B) west\n(C) south\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 272,
    "student_kl": 0.174539,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174539,
    "selection_score": 0.174539,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThe letter G is to J as the letter O is to which letter?\n\nOptions:\n(A) Q\n(B) R\n(C) S\n(D) P<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 262,
    "student_kl": 0.17433,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17433,
    "selection_score": 0.17433,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree of these strings contain only vowels. Which one does not?\n\nOptions:\n(A) aau\n(B) iuo\n(C) aoii\n(D) ddbd<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 191,
    "student_kl": 0.174,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174,
    "selection_score": 0.174,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is May 27, 2023. Spottintreet is 41 days old. What is the date 49 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/07/2023\n(B) 04/08/2023\n(C) 04/05/2023\n(D) 04/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 1476,
    "student_kl": 0.173524,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173524,
    "selection_score": 0.173524,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is April 9, 2024. Frourdtis is 73 days old. What is the date 16 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/26/2024\n(B) 04/24/2024\n(C) 04/22/2024\n(D) 04/25/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 213,
    "student_kl": 0.172663,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172663,
    "selection_score": 0.172663,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Jaysboucklou's favorite colour is not yellow.\n- Jaysboucklou's favorite colour is blue.\n- Pengshaistvear's favorite colour is green.\n\nWhat is Pengshaistvear's favorite colour?\n\nOptions:\n(A) yellow\n(B) blue\n(C) green<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 129,
    "student_kl": 0.16984,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16984,
    "selection_score": 0.16984,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 12-foot fence (irrelevant). You turn left, then turn right, then turn right, then turn around, then turn around. Which direction are you facing?\n\nOptions:\n(A) south\n(B) east\n(C) north\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 173,
    "student_kl": 0.168669,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168669,
    "selection_score": 0.168669,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 13-foot lamp at the origin (irrelevant). You turn right, then turn right, then walk 3 steps forward. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 209,
    "student_kl": 0.168218,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168218,
    "selection_score": 0.168218,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n((False) and (False)) or (False)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 237,
    "student_kl": 0.168208,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168208,
    "selection_score": 0.168208,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 11-foot fence (irrelevant). You walk 5 steps forward, then walk 2 steps forward, then turn around. Which direction are you facing?\n\nOptions:\n(A) east\n(B) west\n(C) north\n(D) south<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 181,
    "student_kl": 0.168127,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168127,
    "selection_score": 0.168127,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is November 18, 2023. Meengthar is 66 days old. What is the date 52 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 09/27/2023\n(B) 09/28/2023\n(C) 09/24/2023\n(D) 09/26/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 495,
    "student_kl": 0.167372,
    "reference_kl": null,
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    "hardness_gap": 0.167372,
    "selection_score": 0.167372,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Pleldweeld's favorite colour is yellow.\n- Gouldvungseng's favorite colour is red.\n- Gouldvungseng's favorite colour is not purple.\n\nWhat is Gouldvungseng's favorite colour?\n\nOptions:\n(A) yellow\n(B) red\n(C) purple<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 212,
    "student_kl": 0.166523,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Joastkack's favorite colour is green.\n- Sweardspait's favorite colour is not yellow.\n- Sweardspait's favorite colour is purple.\n\nWhat is Joastkack's favorite colour?\n\nOptions:\n(A) yellow\n(B) green\n(C) purple<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 215,
    "student_kl": 0.166026,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 10-foot lamp at the origin (irrelevant). You turn right, then turn left, then walk 3 steps forward, then walk 7 steps forward. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 247,
    "student_kl": 0.16568,
    "reference_kl": null,
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    "selection_score": 0.16568,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nJascreld tells the truth. Jascreld says Chayckchoardplourd tells the truth. Chayckchoardplourd says Troacron tells the truth. Troacron says Grietkait tells the truth. Grietkait says Ploustswus tells the truth. A bystander mentions there are 7 people in the room (not relevant). Does Ploustswus tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 375,
    "student_kl": 0.165649,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 5-foot fence (irrelevant). You walk 4 steps forward, then turn left, then turn right. Which direction are you facing?\n\nOptions:\n(A) south\n(B) east\n(C) west\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 230,
    "student_kl": 0.165613,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHayckduck lies. Hayckduck says Theeldmun tells the truth. Theeldmun says Skacrayrieng lies. Skacrayrieng says Skurtgulnald lies. A bystander mentions there are 4 people in the room (not relevant). Does Skurtgulnald tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 374,
    "student_kl": 0.164855,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Hirtjayr's favorite colour is green.\n- Kaicknenspest's favorite colour is yellow.\n- Kaicknenspest's favorite colour is not purple.\n\nWhat is Hirtjayr's favorite colour?\n\nOptions:\n(A) purple\n(B) yellow\n(C) green<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 219,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n((True) or (False)) or (not True)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 212,
    "student_kl": 0.1628,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is September 24, 2024. Kingfri is 13 days old. What is the date 57 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/17/2024\n(B) 11/20/2024\n(C) 11/19/2024\n(D) 11/21/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 452,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
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    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nDrardrat tells the truth. Drardrat says Hanvayncrart tells the truth. Hanvayncrart says Gleangnayng tells the truth. A bystander mentions there are 8 people in the room (not relevant). Does Gleangnayng tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 616,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 350-500 words, explain why incentive design is harder than it looks as if to a curious non-specialist. Use 2-3 paragraphs and ground at least one point with a concrete example.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 512,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on the role of compounding effects in long-term planning. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 460,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on the trade-offs between depth and breadth when reading widely. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 429,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on the role of slack capacity in resilient systems. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on why version control changed how software teams collaborate. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on the trade-off between flexibility and consistency in policy. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
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    "reference_kl": null,
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    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 350-500 words, explain how teams maintain reliability without slowing delivery as if to a curious non-specialist. Use 2-3 paragraphs and ground at least one point with a concrete example.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on why incentive design is harder than it looks. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 512,
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    "reference_kl": null,
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    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 350-500 words, explain why second-order effects often matter more than first-order ones as if to a curious non-specialist. Use 2-3 paragraphs and ground at least one point with a concrete example.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of why retrospective analyses tend to outperform optimistic forecasts. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on how teams maintain reliability without slowing delivery. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 463,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
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  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how why incentive design is harder than it looks works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 512,
    "student_kl": 0.640588,
    "reference_kl": null,
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    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on why honest disagreement is often more useful than polite agreement. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 432,
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    "reference_kl": null,
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    "score_backend": "hf",
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  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 350-500 words, explain why retrospective analyses tend to outperform optimistic forecasts as if to a curious non-specialist. Use 2-3 paragraphs and ground at least one point with a concrete example.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 512,
    "student_kl": 0.62507,
    "reference_kl": null,
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of the trade-offs between specialisation and generalisation in professional careers. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 512,
    "student_kl": 0.622128,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 350-500 words, explain the trade-off between flexibility and consistency in policy as if to a curious non-specialist. Use 2-3 paragraphs and ground at least one point with a concrete example.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 512,
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    "reference_kl": null,
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on the role of constraints in driving creative output. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
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    "continuation_tokens": 383,
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    "selection_mode": "self",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-450 word reflection on how good naming conventions reduce cognitive load. Open with a vivid concrete observation, then connect it to a broader point in a second paragraph, then end with a takeaway sentence.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
    "student_kl": 0.604606,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on the role of compounding effects in long-term planning. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 512,
    "student_kl": 0.602359,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 350-500 words, explain why measurement systems shape the behaviours they're meant to track as if to a curious non-specialist. Use 2-3 paragraphs and ground at least one point with a concrete example.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 512,
    "student_kl": 0.602335,
    "reference_kl": null,
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    "score_backend": "hf",
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  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how how teams maintain reliability without slowing delivery works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 512,
    "student_kl": 0.596562,
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    "axis": "long_form",
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    "selection_score": 0.50518,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on why second-order effects often matter more than first-order ones. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 611,
    "student_kl": 0.504613,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.504613,
    "selection_score": 0.504613,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on how peer review functions as a feedback mechanism. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 620,
    "student_kl": 0.503535,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.503535,
    "selection_score": 0.503535,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of the trade-offs between specialisation and generalisation in professional careers. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 574,
    "student_kl": 0.499503,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.499503,
    "selection_score": 0.499503,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on why honest disagreement is often more useful than polite agreement. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 587,
    "student_kl": 0.486203,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.486203,
    "selection_score": 0.486203,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of how curiosity functions as a self-reinforcing loop. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 511,
    "student_kl": 0.478327,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.478327,
    "selection_score": 0.478327,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on the trade-off between flexibility and consistency in policy. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 564,
    "student_kl": 0.472018,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.472018,
    "selection_score": 0.472018,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on the difference between memorisation and genuine understanding when learning a new skill. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 612,
    "student_kl": 0.432004,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.432004,
    "selection_score": 0.432004,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSlouttrer is planning a 4-night trip with 4 other people, but they're each paying their own way. Slouttrer's lodging costs $80 per night, meals cost $40 per day, and round-trip transport costs $120. How many dollars will Slouttrer's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 512,
    "student_kl": 0.331023,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.331023,
    "selection_score": 0.331023,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCecksnees is planning a 5-night trip with 2 other people, but they're each paying their own way. Cecksnees's lodging costs $150 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Cecksnees's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 512,
    "student_kl": 0.31708,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.31708,
    "selection_score": 0.31708,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFangglays is planning a 4-night trip with 2 other people, but they're each paying their own way. Fangglays's lodging costs $90 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Fangglays's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 512,
    "student_kl": 0.312702,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.312702,
    "selection_score": 0.312702,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nPardjun is planning a 5-night trip with 2 other people, but they're each paying their own way. Pardjun's lodging costs $120 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Pardjun's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 512,
    "student_kl": 0.310766,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.310766,
    "selection_score": 0.310766,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:46 on a 12-hour clock. It runs for 10 hours and 9 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 512,
    "student_kl": 0.303049,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.303049,
    "selection_score": 0.303049,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCrestbird is planning a 3-night trip with 4 other people, but they're each paying their own way. Crestbird's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Crestbird's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 512,
    "student_kl": 0.27729,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.27729,
    "selection_score": 0.27729,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nJaldclat is planning a 3-night trip with 6 other people, but they're each paying their own way. Jaldclat's lodging costs $90 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Jaldclat's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 512,
    "student_kl": 0.264421,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.264421,
    "selection_score": 0.264421,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Thoursnird runs a reading club. 17 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 5 books were returned late. The library charges $5 per late book. They also used the fines to buy 6 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 296,
    "student_kl": 0.256694,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.256694,
    "selection_score": 0.256694,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSmoassnetcur is planning a 7-night trip with 4 other people, but they're each paying their own way. Smoassnetcur's lodging costs $60 per night, meals cost $30 per day, and round-trip transport costs $80. How many dollars will Smoassnetcur's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 512,
    "student_kl": 0.243269,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.243269,
    "selection_score": 0.243269,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA shop has 741 items in stock. They sell 15% of them on Monday, then receive 69 new items. How many items have left the shop, plus the new arrivals (i.e. 15% of 741 plus 69)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 512,
    "student_kl": 0.240661,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.240661,
    "selection_score": 0.240661,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Troatswout runs a reading club. 15 members each borrowed 2 books for the month. The library opens at 12:00 each day. By the deadline, 10 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 367,
    "student_kl": 0.240108,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.240108,
    "selection_score": 0.240108,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA shop has 1021 items in stock. They sell 25% of them on Monday, then receive 17 new items. How many items have left the shop, plus the new arrivals (i.e. 25% of 1021 plus 17)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 512,
    "student_kl": 0.226989,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.226989,
    "selection_score": 0.226989,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Thaytsmurdsald is building 6 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Thaytsmurdsald also orders 20 extra bricks as a safety margin. During delivery, 24 bricks arrive broken and have to be discarded. How many usable bricks does Thaytsmurdsald have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 337,
    "student_kl": 0.212325,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.212325,
    "selection_score": 0.212325,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Glienzissteeld runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 12 books were returned late. The library charges $2 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 243,
    "student_kl": 0.212076,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.212076,
    "selection_score": 0.212076,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Snoskock runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 7 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 292,
    "student_kl": 0.203485,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203485,
    "selection_score": 0.203485,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHockmeeng is planning a 8-night trip with 4 other people, but they're each paying their own way. Hockmeeng's lodging costs $150 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Hockmeeng's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 419,
    "student_kl": 0.202547,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.202547,
    "selection_score": 0.202547,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Theeldsayt runs a reading club. 9 members each borrowed 2 books for the month. The library opens at 12:00 each day. By the deadline, 9 books were returned late. The library charges $3 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 311,
    "student_kl": 0.202312,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.202312,
    "selection_score": 0.202312,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSmoassnetcur is planning a 7-night trip with 4 other people, but they're each paying their own way. Smoassnetcur's lodging costs $60 per night, meals cost $30 per day, and round-trip transport costs $80. How many dollars will Smoassnetcur's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 1024,
    "student_kl": 0.281977,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.281977,
    "selection_score": 0.281977,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSlouttrer is planning a 4-night trip with 4 other people, but they're each paying their own way. Slouttrer's lodging costs $80 per night, meals cost $40 per day, and round-trip transport costs $120. How many dollars will Slouttrer's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 1024,
    "student_kl": 0.271603,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.271603,
    "selection_score": 0.271603,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFangglays is planning a 4-night trip with 2 other people, but they're each paying their own way. Fangglays's lodging costs $90 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Fangglays's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 1024,
    "student_kl": 0.269258,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.269258,
    "selection_score": 0.269258,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCrestbird is planning a 3-night trip with 4 other people, but they're each paying their own way. Crestbird's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Crestbird's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 1024,
    "student_kl": 0.260384,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.260384,
    "selection_score": 0.260384,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nDoarzoungnieng is planning a 5-night trip with 6 other people, but they're each paying their own way. Doarzoungnieng's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Doarzoungnieng's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 1024,
    "student_kl": 0.259213,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.259213,
    "selection_score": 0.259213,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Troatswout runs a reading club. 15 members each borrowed 2 books for the month. The library opens at 12:00 each day. By the deadline, 10 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 329,
    "student_kl": 0.251436,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.251436,
    "selection_score": 0.251436,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCecksnees is planning a 5-night trip with 2 other people, but they're each paying their own way. Cecksnees's lodging costs $150 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Cecksnees's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 1024,
    "student_kl": 0.244836,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.244836,
    "selection_score": 0.244836,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:30 on a 12-hour clock. It runs for 4 hours and 15 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 1024,
    "student_kl": 0.240857,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.240857,
    "selection_score": 0.240857,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nJaldclat is planning a 3-night trip with 6 other people, but they're each paying their own way. Jaldclat's lodging costs $90 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Jaldclat's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 1024,
    "student_kl": 0.239004,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.239004,
    "selection_score": 0.239004,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHockmeeng is planning a 8-night trip with 4 other people, but they're each paying their own way. Hockmeeng's lodging costs $150 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Hockmeeng's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 682,
    "student_kl": 0.236947,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.236947,
    "selection_score": 0.236947,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Thaytsmurdsald is building 6 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Thaytsmurdsald also orders 20 extra bricks as a safety margin. During delivery, 24 bricks arrive broken and have to be discarded. How many usable bricks does Thaytsmurdsald have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 323,
    "student_kl": 0.234757,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.234757,
    "selection_score": 0.234757,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nPardjun is planning a 5-night trip with 2 other people, but they're each paying their own way. Pardjun's lodging costs $120 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Pardjun's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 1024,
    "student_kl": 0.233597,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233597,
    "selection_score": 0.233597,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nMirfield is planning a 4-night trip with 4 other people, but they're each paying their own way. Mirfield's lodging costs $80 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Mirfield's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 460,
    "student_kl": 0.226815,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.226815,
    "selection_score": 0.226815,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Theeldsayt runs a reading club. 9 members each borrowed 2 books for the month. The library opens at 12:00 each day. By the deadline, 9 books were returned late. The library charges $3 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 302,
    "student_kl": 0.218382,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.218382,
    "selection_score": 0.218382,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Thoursnird runs a reading club. 17 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 5 books were returned late. The library charges $5 per late book. They also used the fines to buy 6 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 322,
    "student_kl": 0.217102,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.217102,
    "selection_score": 0.217102,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA shop has 741 items in stock. They sell 15% of them on Monday, then receive 69 new items. How many items have left the shop, plus the new arrivals (i.e. 15% of 741 plus 69)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 1024,
    "student_kl": 0.215882,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.215882,
    "selection_score": 0.215882,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Snoskock runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 7 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 300,
    "student_kl": 0.213221,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.213221,
    "selection_score": 0.213221,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA shop has 1021 items in stock. They sell 25% of them on Monday, then receive 17 new items. How many items have left the shop, plus the new arrivals (i.e. 25% of 1021 plus 17)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 1024,
    "student_kl": 0.212638,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.212638,
    "selection_score": 0.212638,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:46 on a 12-hour clock. It runs for 10 hours and 9 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 589,
    "student_kl": 0.212537,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.212537,
    "selection_score": 0.212537,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA shop has 582 items in stock. They sell 15% of them on Monday, then receive 20 new items. How many items have left the shop, plus the new arrivals (i.e. 15% of 582 plus 20)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 1024,
    "student_kl": 0.203404,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203404,
    "selection_score": 0.203404,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA shop has 448 items in stock. They sell 40% of them on Monday, then receive 15 new items. How many items have left the shop, plus the new arrivals (i.e. 40% of 448 plus 15)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 843,
    "student_kl": 0.199554,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.199554,
    "selection_score": 0.199554,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Glienzissteeld runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 12 books were returned late. The library charges $2 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 304,
    "student_kl": 0.194955,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.194955,
    "selection_score": 0.194955,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 07:28 on a 12-hour clock. It runs for 7 hours and 54 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 952,
    "student_kl": 0.189465,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189465,
    "selection_score": 0.189465,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Destfegeal is building 3 brick walls using a 8-foot ladder. Each wall needs 80 bricks. Destfegeal also orders 50 extra bricks as a safety margin. During delivery, 22 bricks arrive broken and have to be discarded. How many usable bricks does Destfegeal have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 338,
    "student_kl": 0.189117,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189117,
    "selection_score": 0.189117,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 5 hours and 54 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 217,
    "student_kl": 0.184147,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.184147,
    "selection_score": 0.184147,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Laickshurdchayld is building 4 brick walls using a 8-foot ladder. Each wall needs 120 bricks. Laickshurdchayld also orders 30 extra bricks as a safety margin. During delivery, 17 bricks arrive broken and have to be discarded. How many usable bricks does Laickshurdchayld have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 505,
    "student_kl": 0.183376,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.183376,
    "selection_score": 0.183376,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA shop has 280 items in stock. They sell 25% of them on Monday, then receive 12 new items. How many items have left the shop, plus the new arrivals (i.e. 25% of 280 plus 12)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 436,
    "student_kl": 0.180303,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180303,
    "selection_score": 0.180303,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nStartgleeld ran a 7-hour charity fundraiser. 8 silver-tier donors gave $25 each. 8 gold-tier donors gave $50 each. A local company contributed an additional $200 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 305,
    "student_kl": 0.180222,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180222,
    "selection_score": 0.180222,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Sieldcraist's hockey team played 8 games with 6 players on the field at any time. They won 3 games and lost 5 games. Each win is worth 2 league points, each loss is worth 1 consolation points, and the team got an extra 6 bonus points for fair play. How many total league points did Sieldcraist's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 484,
    "student_kl": 0.179923,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179923,
    "selection_score": 0.179923,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nKaystswer goes to the dartslolshop with $50. Their friend Voaststiel, who is 7 years old, comes along but doesn't buy anything. Kaystswer buys 5 smolkeels at $8 each and 6 trouvuts at $6 each. How many dollars does Kaystswer have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 286,
    "student_kl": 0.179156,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179156,
    "selection_score": 0.179156,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Leerdflist runs a reading club. 17 members each borrowed 2 books for the month. The library opens at 15:00 each day. By the deadline, 10 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 281,
    "student_kl": 0.178349,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178349,
    "selection_score": 0.178349,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nTeacher Satfreer runs an after-school program with 3 classes. Each class has 28 students enrolled, but on Monday 2 students in each class were absent. 3 parent volunteers also stayed to help. The school district has 9 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 241,
    "student_kl": 0.172453,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172453,
    "selection_score": 0.172453,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Braickzieck is building 8 brick walls using a 10-foot ladder. Each wall needs 200 bricks. Braickzieck also orders 20 extra bricks as a safety margin. During delivery, 17 bricks arrive broken and have to be discarded. How many usable bricks does Braickzieck have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 288,
    "student_kl": 0.172291,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172291,
    "selection_score": 0.172291,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Prunghoung is building 4 brick walls using a 12-foot ladder. Each wall needs 120 bricks. Prunghoung also orders 50 extra bricks as a safety margin. During delivery, 7 bricks arrive broken and have to be discarded. How many usable bricks does Prunghoung have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 290,
    "student_kl": 0.165419,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165419,
    "selection_score": 0.165419,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 6 hours and 7 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 234,
    "student_kl": 0.164192,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.164192,
    "selection_score": 0.164192,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nPirthourtgrierd drives east on the highway at 50 mph for 5 hours. They stop at a rest area, then drive another 33 miles north to pick up a friend. From there, they continue at 75 mph for 2 hours. The car holds 24 gallons of fuel. How many miles total has Pirthourtgrierd driven?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 469,
    "student_kl": 0.162718,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162718,
    "selection_score": 0.162718,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Floustlos's rugby team played 12 games with 5 players on the field at any time. They won 5 games and lost 7 games. Each win is worth 2 league points, each loss is worth 0 consolation points, and the team got an extra 4 bonus points for fair play. How many total league points did Floustlos's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 461,
    "student_kl": 0.162373,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162373,
    "selection_score": 0.162373,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 8 servings and uses 5 cups of flour. Hulourd wants to make 24 servings for a school bake sale. They also need to add 7 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Hulourd need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 377,
    "student_kl": 0.161665,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161665,
    "selection_score": 0.161665,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Proardpreermeack is building 5 brick walls using a 12-foot ladder. Each wall needs 120 bricks. Proardpreermeack also orders 30 extra bricks as a safety margin. During delivery, 17 bricks arrive broken and have to be discarded. How many usable bricks does Proardpreermeack have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 408,
    "student_kl": 0.16038,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16038,
    "selection_score": 0.16038,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nDoardcairtkos drives east on the highway at 60 mph for 4 hours. They stop at a rest area, then drive another 40 miles north to pick up a friend. From there, they continue at 65 mph for 3 hours. The car holds 8 gallons of fuel. How many miles total has Doardcairtkos driven?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 437,
    "student_kl": 0.15375,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.15375,
    "selection_score": 0.15375,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLayscrir keeps 11 chickens in a 15-meter coop. Each chicken lays 6 eggs per week. Over 3 weeks, the family ate 24 eggs for breakfast and donated 14 eggs to a neighbor. How many eggs are left at the end of the 3 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 321,
    "student_kl": 0.153523,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.153523,
    "selection_score": 0.153523,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nGlangroack drives east on the highway at 70 mph for 2 hours. They stop at a rest area, then drive another 28 miles north to pick up a friend. From there, they continue at 45 mph for 3 hours. The car holds 12 gallons of fuel. How many miles total has Glangroack driven?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 534,
    "student_kl": 0.153053,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.153053,
    "selection_score": 0.153053,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Hiestsmieck is building 4 brick walls using a 12-foot ladder. Each wall needs 80 bricks. Hiestsmieck also orders 30 extra bricks as a safety margin. During delivery, 21 bricks arrive broken and have to be discarded. How many usable bricks does Hiestsmieck have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 380,
    "student_kl": 0.152462,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.152462,
    "selection_score": 0.152462,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCompute 16! mod 17. (That is, the remainder when 16 factorial is divided by 17.)\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 383,
    "student_kl": 0.152038,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.152038,
    "selection_score": 0.152038,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nTeacher Chourtgrel runs an after-school program with 6 classes. Each class has 28 students enrolled, but on Monday 3 students in each class were absent. 5 parent volunteers also stayed to help. The school district has 11 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 264,
    "student_kl": 0.151673,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.151673,
    "selection_score": 0.151673,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLoungstolswean ran a 7-hour charity fundraiser. 16 silver-tier donors gave $20 each. 7 gold-tier donors gave $100 each. A local company contributed an additional $300 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 285,
    "student_kl": 0.150985,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.150985,
    "selection_score": 0.150985,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSnonsnoun ran a 5-hour charity fundraiser. 24 silver-tier donors gave $20 each. 5 gold-tier donors gave $100 each. A local company contributed an additional $100 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 415,
    "student_kl": 0.150494,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.150494,
    "selection_score": 0.150494,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nTeacher Pliszoasniet runs an after-school program with 3 classes. Each class has 30 students enrolled, but on Monday 3 students in each class were absent. 5 parent volunteers also stayed to help. The school district has 11 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 280,
    "student_kl": 0.150294,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.150294,
    "selection_score": 0.150294,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 6 servings and uses 5 cups of flour. Nertgleart wants to make 24 servings for a school bake sale. They also need to add 3 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Nertgleart need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 402,
    "student_kl": 0.150051,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.150051,
    "selection_score": 0.150051,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Gleeckfreack's rugby team played 11 games with 6 players on the field at any time. They won 3 games and lost 8 games. Each win is worth 2 league points, each loss is worth 1 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Gleeckfreack's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 347,
    "student_kl": 0.148008,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.148008,
    "selection_score": 0.148008,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 4 servings and uses 3 cups of flour. Taystlist wants to make 16 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 450 degrees, but that doesn't change the recipe. How many total cups of flour does Taystlist need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 430,
    "student_kl": 0.147606,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.147606,
    "selection_score": 0.147606,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSheengwick ran a 5-hour charity fundraiser. 12 silver-tier donors gave $20 each. 3 gold-tier donors gave $75 each. A local company contributed an additional $300 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 374,
    "student_kl": 0.145868,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.145868,
    "selection_score": 0.145868,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA biscuits recipe makes 6 servings and uses 2 cups of flour. Mulsus wants to make 24 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Mulsus need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 467,
    "student_kl": 0.145521,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.145521,
    "selection_score": 0.145521,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCeenneassmis keeps 15 chickens in a 12-meter coop. Each chicken lays 4 eggs per week. Over 4 weeks, the family ate 12 eggs for breakfast and donated 11 eggs to a neighbor. How many eggs are left at the end of the 4 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 448,
    "student_kl": 0.144534,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.144534,
    "selection_score": 0.144534,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSwinsmer ran a 7-hour charity fundraiser. 11 silver-tier donors gave $25 each. 4 gold-tier donors gave $100 each. A local company contributed an additional $200 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 293,
    "student_kl": 0.143164,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.143164,
    "selection_score": 0.143164,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nGrayrdshastflier goes to the seecksnairtstand with $100. Their friend Putflirt, who is 7 years old, comes along but doesn't buy anything. Grayrdshastflier buys 3 dungsneas at $2 each and 3 brounthoungs at $8 each. How many dollars does Grayrdshastflier have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 389,
    "student_kl": 0.142634,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.142634,
    "selection_score": 0.142634,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA pancakes recipe makes 6 servings and uses 2 cups of flour. Skourdmoardcrit wants to make 18 servings for a school bake sale. They also need to add 3 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Skourdmoardcrit need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 387,
    "student_kl": 0.141768,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.141768,
    "selection_score": 0.141768,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nTardstor keeps 23 chickens in a 18-meter coop. Each chicken lays 6 eggs per week. Over 2 weeks, the family ate 24 eggs for breakfast and donated 18 eggs to a neighbor. How many eggs are left at the end of the 2 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 315,
    "student_kl": 0.140785,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.140785,
    "selection_score": 0.140785,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nGlurdtheal ran a 5-hour charity fundraiser. 11 silver-tier donors gave $10 each. 8 gold-tier donors gave $75 each. A local company contributed an additional $200 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 292,
    "student_kl": 0.140222,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.140222,
    "selection_score": 0.140222,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSlaldpourtshuld goes to the droldstaisstand with $120. Their friend Louldgreasgoat, who is 14 years old, comes along but doesn't buy anything. Slaldpourtshuld buys 5 steatfliests at $8 each and 4 gloasthiengs at $5 each. How many dollars does Slaldpourtshuld have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 283,
    "student_kl": 0.138289,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.138289,
    "selection_score": 0.138289,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nIn a class, 60 students study Spanish, 59 study French, and 41 study both. How many students study Spanish or French (or both)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 396,
    "student_kl": 0.13828,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.13828,
    "selection_score": 0.13828,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA bag contains 9 red, 2 blue, and 4 green marbles. You draw one at random. What is the probability (in whole percent, rounded down) of drawing a red marble?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 373,
    "student_kl": 0.136828,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.136828,
    "selection_score": 0.136828,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHockmeeng is planning a 8-night trip with 4 other people, but they're each paying their own way. Hockmeeng's lodging costs $150 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Hockmeeng's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 2048,
    "student_kl": 0.310209,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.310209,
    "selection_score": 0.310209,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nPardjun is planning a 5-night trip with 2 other people, but they're each paying their own way. Pardjun's lodging costs $120 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Pardjun's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 2048,
    "student_kl": 0.301445,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.301445,
    "selection_score": 0.301445,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCecksnees is planning a 5-night trip with 2 other people, but they're each paying their own way. Cecksnees's lodging costs $150 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Cecksnees's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 2048,
    "student_kl": 0.285741,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.285741,
    "selection_score": 0.285741,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSmoassnetcur is planning a 7-night trip with 4 other people, but they're each paying their own way. Smoassnetcur's lodging costs $60 per night, meals cost $30 per day, and round-trip transport costs $80. How many dollars will Smoassnetcur's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 1054,
    "student_kl": 0.280224,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.280224,
    "selection_score": 0.280224,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nMirfield is planning a 4-night trip with 4 other people, but they're each paying their own way. Mirfield's lodging costs $80 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Mirfield's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 1175,
    "student_kl": 0.277078,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.277078,
    "selection_score": 0.277078,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCrestbird is planning a 3-night trip with 4 other people, but they're each paying their own way. Crestbird's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Crestbird's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 1595,
    "student_kl": 0.262243,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.262243,
    "selection_score": 0.262243,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSlouttrer is planning a 4-night trip with 4 other people, but they're each paying their own way. Slouttrer's lodging costs $80 per night, meals cost $40 per day, and round-trip transport costs $120. How many dollars will Slouttrer's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 1912,
    "student_kl": 0.258924,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.258924,
    "selection_score": 0.258924,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nDoarzoungnieng is planning a 5-night trip with 6 other people, but they're each paying their own way. Doarzoungnieng's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Doarzoungnieng's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 1511,
    "student_kl": 0.233789,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233789,
    "selection_score": 0.233789,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Glienzissteeld runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 12 books were returned late. The library charges $2 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 251,
    "student_kl": 0.231278,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.231278,
    "selection_score": 0.231278,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA shop has 582 items in stock. They sell 15% of them on Monday, then receive 20 new items. How many items have left the shop, plus the new arrivals (i.e. 15% of 582 plus 20)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 1382,
    "student_kl": 0.227177,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.227177,
    "selection_score": 0.227177,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Troatswout runs a reading club. 15 members each borrowed 2 books for the month. The library opens at 12:00 each day. By the deadline, 10 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 281,
    "student_kl": 0.224148,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.224148,
    "selection_score": 0.224148,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:46 on a 12-hour clock. It runs for 10 hours and 9 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 1273,
    "student_kl": 0.220882,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.220882,
    "selection_score": 0.220882,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Thoursnird runs a reading club. 17 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 5 books were returned late. The library charges $5 per late book. They also used the fines to buy 6 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 300,
    "student_kl": 0.219785,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219785,
    "selection_score": 0.219785,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Hiestsmieck is building 4 brick walls using a 12-foot ladder. Each wall needs 80 bricks. Hiestsmieck also orders 30 extra bricks as a safety margin. During delivery, 21 bricks arrive broken and have to be discarded. How many usable bricks does Hiestsmieck have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 380,
    "student_kl": 0.215958,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.215958,
    "selection_score": 0.215958,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nJaldclat is planning a 3-night trip with 6 other people, but they're each paying their own way. Jaldclat's lodging costs $90 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Jaldclat's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 2048,
    "student_kl": 0.215623,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.215623,
    "selection_score": 0.215623,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA shop has 448 items in stock. They sell 40% of them on Monday, then receive 15 new items. How many items have left the shop, plus the new arrivals (i.e. 40% of 448 plus 15)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 1594,
    "student_kl": 0.211742,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.211742,
    "selection_score": 0.211742,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:30 on a 12-hour clock. It runs for 4 hours and 15 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 579,
    "student_kl": 0.210833,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.210833,
    "selection_score": 0.210833,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA shop has 741 items in stock. They sell 15% of them on Monday, then receive 69 new items. How many items have left the shop, plus the new arrivals (i.e. 15% of 741 plus 69)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 916,
    "student_kl": 0.210017,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.210017,
    "selection_score": 0.210017,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Snoskock runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 7 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 321,
    "student_kl": 0.209606,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.209606,
    "selection_score": 0.209606,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFangglays is planning a 4-night trip with 2 other people, but they're each paying their own way. Fangglays's lodging costs $90 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Fangglays's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 2048,
    "student_kl": 0.208133,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.208133,
    "selection_score": 0.208133,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Leerdflist runs a reading club. 17 members each borrowed 2 books for the month. The library opens at 15:00 each day. By the deadline, 10 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 302,
    "student_kl": 0.20154,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.20154,
    "selection_score": 0.20154,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCaptain Floustlos's rugby team played 12 games with 5 players on the field at any time. They won 5 games and lost 7 games. Each win is worth 2 league points, each loss is worth 0 consolation points, and the team got an extra 4 bonus points for fair play. How many total league points did Floustlos's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 347,
    "student_kl": 0.191099,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.191099,
    "selection_score": 0.191099,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Theeldsayt runs a reading club. 9 members each borrowed 2 books for the month. The library opens at 12:00 each day. By the deadline, 9 books were returned late. The library charges $3 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 256,
    "student_kl": 0.189233,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189233,
    "selection_score": 0.189233,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nJeerkeart keeps 15 chickens in a 12-meter coop. Each chicken lays 7 eggs per week. Over 2 weeks, the family ate 20 eggs for breakfast and donated 15 eggs to a neighbor. How many eggs are left at the end of the 2 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 313,
    "student_kl": 0.185015,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185015,
    "selection_score": 0.185015,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Kasjourd is building 3 brick walls using a 10-foot ladder. Each wall needs 100 bricks. Kasjourd also orders 30 extra bricks as a safety margin. During delivery, 13 bricks arrive broken and have to be discarded. How many usable bricks does Kasjourd have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 305,
    "student_kl": 0.181527,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.181527,
    "selection_score": 0.181527,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCaptain Brelsnockmin's basketball team played 18 games with 7 players on the field at any time. They won 9 games and lost 9 games. Each win is worth 2 league points, each loss is worth 0 consolation points, and the team got an extra 8 bonus points for fair play. How many total league points did Brelsnockmin's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 320,
    "student_kl": 0.175551,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175551,
    "selection_score": 0.175551,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA shop has 1021 items in stock. They sell 25% of them on Monday, then receive 17 new items. How many items have left the shop, plus the new arrivals (i.e. 25% of 1021 plus 17)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 879,
    "student_kl": 0.174542,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174542,
    "selection_score": 0.174542,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nDurtshenglel keeps 20 chickens in a 12-meter coop. Each chicken lays 6 eggs per week. Over 6 weeks, the family ate 25 eggs for breakfast and donated 16 eggs to a neighbor. How many eggs are left at the end of the 6 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 326,
    "student_kl": 0.172249,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172249,
    "selection_score": 0.172249,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 8 servings and uses 5 cups of flour. Hulourd wants to make 24 servings for a school bake sale. They also need to add 7 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Hulourd need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 401,
    "student_kl": 0.170022,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170022,
    "selection_score": 0.170022,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Thaytsmurdsald is building 6 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Thaytsmurdsald also orders 20 extra bricks as a safety margin. During delivery, 24 bricks arrive broken and have to be discarded. How many usable bricks does Thaytsmurdsald have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 438,
    "student_kl": 0.169399,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169399,
    "selection_score": 0.169399,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Destfegeal is building 3 brick walls using a 8-foot ladder. Each wall needs 80 bricks. Destfegeal also orders 50 extra bricks as a safety margin. During delivery, 22 bricks arrive broken and have to be discarded. How many usable bricks does Destfegeal have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 290,
    "student_kl": 0.16651,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16651,
    "selection_score": 0.16651,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Prunghoung is building 4 brick walls using a 12-foot ladder. Each wall needs 120 bricks. Prunghoung also orders 50 extra bricks as a safety margin. During delivery, 7 bricks arrive broken and have to be discarded. How many usable bricks does Prunghoung have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 343,
    "student_kl": 0.163516,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163516,
    "selection_score": 0.163516,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nTwo cars start traveling east on the same highway. Car A travels at 58 kilometers per hour. Car B starts 23 kilometers behind Car A and travels at 84 kilometers per hour. After 8 hours of driving, how many kilometers ahead of Car A is Car B?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 932,
    "student_kl": 0.161363,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161363,
    "selection_score": 0.161363,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "tool_use",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 6 hours and 7 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 227,
    "student_kl": 0.160422,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.160422,
    "selection_score": 0.160422,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 277,
    "student_kl": 0.250262,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.250262,
    "selection_score": 0.250262,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef digital_root(n):\n    \"\"\"Return the digital root of the non-negative integer ``n``: repeatedly sum the decimal digits until the result has a single digit.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 64,
    "student_kl": 0.240523,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.240523,
    "selection_score": 0.240523,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 25, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 294,
    "student_kl": 0.208367,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.208367,
    "selection_score": 0.208367,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 139,
    "student_kl": 0.200441,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.200441,
    "selection_score": 0.200441,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_min(xs):\n    \"\"\"Return a list of the minimums of every contiguous window of exactly 2 elements in ``xs``. If ``xs`` has fewer than 2 elements, return []. The output has length ``max(0, len(xs) - 2 + 1)``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 22,
    "student_kl": 0.186849,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186849,
    "selection_score": 0.186849,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 210,
    "student_kl": 0.185661,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185661,
    "selection_score": 0.185661,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 5, 10, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 113,
    "student_kl": 0.17914,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17914,
    "selection_score": 0.17914,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 10]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 170,
    "student_kl": 0.163019,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163019,
    "selection_score": 0.163019,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 62,
    "student_kl": 0.157151,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.157151,
    "selection_score": 0.157151,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef unique_paths(m, n):\n    \"\"\"Return the number of unique paths from the top-left corner to the bottom-right corner of an ``m \u00d7 n`` grid where you can only move right or down at each step. ``m`` and ``n`` are positive integers.\n\n    >>> unique_paths(2, 2)\n    2\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 163,
    "student_kl": 0.141081,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.141081,
    "selection_score": 0.141081,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 10, 20, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 174,
    "student_kl": 0.139364,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.139364,
    "selection_score": 0.139364,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef repeat_chars(s):\n    \"\"\"Return a string where every character of ``s`` is repeated 4 times in place. ``repeat_chars('ab')`` is ``'aaaabbbb'``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.137616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.137616,
    "selection_score": 0.137616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_max_sum(xs, k):\n    \"\"\"Return the maximum sum of any contiguous window of exactly ``k`` consecutive elements in the list ``xs``. If ``k`` is larger than the length of ``xs`` or ``xs`` is empty, return 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 85,
    "student_kl": 0.130989,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.130989,
    "selection_score": 0.130989,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 93,
    "student_kl": 0.265918,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.265918,
    "selection_score": 0.265918,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 294,
    "student_kl": 0.238256,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.238256,
    "selection_score": 0.238256,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef swap_pairs(s):\n    \"\"\"Return a string where every pair of adjacent characters has been swapped (so ``'abcd'`` becomes ``'badc'``). If the length is odd, the trailing character stays in place.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 50,
    "student_kl": 0.191966,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.191966,
    "selection_score": 0.191966,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 150,
    "student_kl": 0.190574,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190574,
    "selection_score": 0.190574,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef unique_paths(m, n):\n    \"\"\"Return the number of unique paths from the top-left corner to the bottom-right corner of an ``m \u00d7 n`` grid where you can only move right or down at each step. ``m`` and ``n`` are positive integers.\n\n    >>> unique_paths(2, 2)\n    2\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 99,
    "student_kl": 0.157056,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.157056,
    "selection_score": 0.157056,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 2, 20]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 162,
    "student_kl": 0.153683,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.153683,
    "selection_score": 0.153683,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef digital_root(n):\n    \"\"\"Return the digital root of the non-negative integer ``n``: repeatedly sum the decimal digits until the result has a single digit.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 27,
    "student_kl": 0.151465,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.151465,
    "selection_score": 0.151465,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 5, 10]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 105,
    "student_kl": 0.147124,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.147124,
    "selection_score": 0.147124,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 143,
    "student_kl": 0.142648,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.142648,
    "selection_score": 0.142648,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 25, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 155,
    "student_kl": 0.137689,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.137689,
    "selection_score": 0.137689,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef repeat_chars(s):\n    \"\"\"Return a string where every character of ``s`` is repeated 4 times in place. ``repeat_chars('ab')`` is ``'aaaabbbb'``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.137616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.137616,
    "selection_score": 0.137616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef repeat_chars(s):\n    \"\"\"Return a string where every character of ``s`` is repeated 2 times in place. ``repeat_chars('ab')`` is ``'aabb'``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 13,
    "student_kl": 0.137001,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.137001,
    "selection_score": 0.137001,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_max_sum(xs, k):\n    \"\"\"Return the maximum sum of any contiguous window of exactly ``k`` consecutive elements in the list ``xs``. If ``k`` is larger than the length of ``xs`` or ``xs`` is empty, return 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 85,
    "student_kl": 0.133877,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.133877,
    "selection_score": 0.133877,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 5, 10, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 168,
    "student_kl": 0.131774,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.131774,
    "selection_score": 0.131774,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef aggregate(xs):\n    \"\"\"Return the product of the non-zero elements of ``xs``. If every element is zero, return 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 52,
    "student_kl": 0.124755,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.124755,
    "selection_score": 0.124755,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef is_anagram(a, b):\n    \"\"\"Return True if string ``a`` is an anagram of string ``b`` (case-sensitive). Different lengths return False.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 24,
    "student_kl": 0.114493,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.114493,
    "selection_score": 0.114493,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef rolling_max(xs):\n    \"\"\"Return a list where the i-th element is the maximum of the last 2 elements of ``xs`` ending at index i (inclusive). For i < 1, use whatever elements are available (i.e. the prefix). The output has the same length as ``xs``. Empty input returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 51,
    "student_kl": 0.110089,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.110089,
    "selection_score": 0.110089,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 10]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 193,
    "student_kl": 0.109147,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.109147,
    "selection_score": 0.109147,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 10, 20, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 165,
    "student_kl": 0.107271,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.107271,
    "selection_score": 0.107271,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_min(xs):\n    \"\"\"Return a list of the minimums of every contiguous window of exactly 2 elements in ``xs``. If ``xs`` has fewer than 2 elements, return []. The output has length ``max(0, len(xs) - 2 + 1)``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 39,
    "student_kl": 0.099771,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.099771,
    "selection_score": 0.099771,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_min(xs):\n    \"\"\"Return a list of the minimums of every contiguous window of exactly 3 elements in ``xs``. If ``xs`` has fewer than 3 elements, return []. The output has length ``max(0, len(xs) - 3 + 1)``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 36,
    "student_kl": 0.094716,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.094716,
    "selection_score": 0.094716,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef count_divisors(n):\n    \"\"\"Return the number of positive divisors of the positive integer ``n`` (including 1 and ``n`` itself).\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 66,
    "student_kl": 0.09469,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.09469,
    "selection_score": 0.09469,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef aggregate(xs):\n    \"\"\"Return the number of strictly positive elements of ``xs``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 16,
    "student_kl": 0.091323,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.091323,
    "selection_score": 0.091323,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 10, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 168,
    "student_kl": 0.089524,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.089524,
    "selection_score": 0.089524,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef transform(xs):\n    \"\"\"Return a list where every element of ``xs`` is doubled.\n\n    >>> transform([1, 2, 3])\n    [2, 4, 6]\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 13,
    "student_kl": 0.086387,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.086387,
    "selection_score": 0.086387,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef eval_rpn(tokens):\n    \"\"\"Evaluate the expression in Reverse Polish Notation given as a list of tokens. Each token is either an integer (Python int) or one of the operators '+', '-', '*'. Division is not used. Return the integer result. The expression is well-formed.\n\n    >>> eval_rpn([2, 3, '+'])\n    5\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 98,
    "student_kl": 0.086117,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.086117,
    "selection_score": 0.086117,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef rolling_max(xs):\n    \"\"\"Return a list where the i-th element is the maximum of the last 4 elements of ``xs`` ending at index i (inclusive). For i < 3, use whatever elements are available (i.e. the prefix). The output has the same length as ``xs``. Empty input returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 53,
    "student_kl": 0.084755,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.084755,
    "selection_score": 0.084755,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef split_paren_groups(s):\n    \"\"\"The input is a string containing only '(' and ')' characters and spaces. The parentheses form one or more balanced groups concatenated (possibly separated by spaces, which should be ignored). Return a list of the balanced groups in order, with all spaces removed. Each output group is itself balanced. The empty input returns [].\n\n    >>> split_paren_groups('( ) (( ))')\n    ['()', '(())']\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 118,
    "student_kl": 0.080443,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.080443,
    "selection_score": 0.080443,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef compress(s):\n    \"\"\"Return a run-length-encoded version of ``s`` of the form 'a3b2c4' (character followed by run length, with run length=1 also written as 'a1'). If the encoded form is not strictly shorter than the original, return the original string instead. Empty input returns ''.\n\n    >>> compress('aaabbc')\n    'a3b2c1'\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 131,
    "student_kl": 0.079383,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.079383,
    "selection_score": 0.079383,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef transform(xs):\n    \"\"\"Return a list where every element of ``xs`` is negated.\n\n    >>> transform([1, -2, 3])\n    [-1, 2, -3]\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 10,
    "student_kl": 0.078916,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.078916,
    "selection_score": 0.078916,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef two_sum_indices(xs):\n    \"\"\"Return a sorted list of all unordered pairs (i, j) with i < j such that ``xs[i] + xs[j] == 10``. Pairs are tuples. The output is sorted by (i, j). Empty result returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 61,
    "student_kl": 0.077984,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.077984,
    "selection_score": 0.077984,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef rolling_max(xs):\n    \"\"\"Return a list where the i-th element is the maximum of the last 3 elements of ``xs`` ending at index i (inclusive). For i < 2, use whatever elements are available (i.e. the prefix). The output has the same length as ``xs``. Empty input returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 53,
    "student_kl": 0.077747,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.077747,
    "selection_score": 0.077747,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef two_sum_indices(xs):\n    \"\"\"Return a sorted list of all unordered pairs (i, j) with i < j such that ``xs[i] + xs[j] == 9``. Pairs are tuples. The output is sorted by (i, j). Empty result returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 60,
    "student_kl": 0.077427,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.077427,
    "selection_score": 0.077427,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef is_balanced_multi(s):\n    \"\"\"Return True iff every opening bracket in ``s`` has a matching closing bracket of the same type and they are properly nested. The bracket types are '()', '[]', and '{}'. Other characters are ignored. Empty string is True.\n\n    >>> is_balanced_multi('([{}])')\n    True\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 84,
    "student_kl": 0.07524,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.07524,
    "selection_score": 0.07524,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef longest_unique(s):\n    \"\"\"Return the length of the longest contiguous substring of ``s`` containing no repeated characters. Empty string returns 0.\n\n    >>> longest_unique('abcabcbb')\n    3\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 96,
    "student_kl": 0.07307,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.07307,
    "selection_score": 0.07307,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef merge(intervals):\n    \"\"\"Given a list of [start, end] integer intervals (closed on both ends), return a new list of merged, non-overlapping intervals sorted by start. Two intervals are considered overlapping if they share at least one integer. Empty input returns []. Singletons (start==end) are allowed.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 104,
    "student_kl": 0.071023,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.071023,
    "selection_score": 0.071023,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef aggregate(xs):\n    \"\"\"Return the sum of the even integers in ``xs``.\n\n    If there are no even integers, return 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 18,
    "student_kl": 0.068952,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.068952,
    "selection_score": 0.068952,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef two_sum_indices(xs):\n    \"\"\"Return a sorted list of all unordered pairs (i, j) with i < j such that ``xs[i] + xs[j] == 11``. Pairs are tuples. The output is sorted by (i, j). Empty result returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 63,
    "student_kl": 0.06887,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.06887,
    "selection_score": 0.06887,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef two_sum_indices(xs):\n    \"\"\"Return a sorted list of all unordered pairs (i, j) with i < j such that ``xs[i] + xs[j] == 12``. Pairs are tuples. The output is sorted by (i, j). Empty result returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 66,
    "student_kl": 0.063706,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.063706,
    "selection_score": 0.063706,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef transform(xs):\n    \"\"\"Return a list of the absolute values of each element of ``xs``.\n\n    >>> transform([-1, 2, -3])\n    [1, 2, 3]\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 12,
    "student_kl": 0.061869,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.061869,
    "selection_score": 0.061869,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef two_sum_indices(xs):\n    \"\"\"Return a sorted list of all unordered pairs (i, j) with i < j such that ``xs[i] + xs[j] == 3``. Pairs are tuples. The output is sorted by (i, j). Empty result returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 65,
    "student_kl": 0.055982,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.055982,
    "selection_score": 0.055982,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef pair_count(xs):\n    \"\"\"Return the number of unordered pairs (i, j) with i < j such that ``xs[i] + xs[j] == 10``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 54,
    "student_kl": 0.053233,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.053233,
    "selection_score": 0.053233,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef first_index(xs, target):\n    \"\"\"Given a non-decreasing list of integers ``xs`` and an integer ``target``, return the leftmost index ``i`` such that ``xs[i] == target``. If ``target`` is not present, return -1. Run in O(log n).\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 95,
    "student_kl": 0.051643,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.051643,
    "selection_score": 0.051643,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef roman_to_int(s):\n    \"\"\"Convert a valid roman numeral string ``s`` (using I, V, X, L, C, D, M with the standard subtractive notation IV, IX, XL, XC, CD, CM) to its integer value. Input is in the range 1..3999. Empty string returns 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 146,
    "student_kl": 0.048403,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.048403,
    "selection_score": 0.048403,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef rle(s):\n    \"\"\"Return the run-length encoding of the string ``s`` as a list of (char, count) tuples. ``rle('')`` is ``[]``. ``rle('aaabb')`` is ``[('a', 3), ('b', 2)]``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 94,
    "student_kl": 0.04744,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.04744,
    "selection_score": 0.04744,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 10, 20, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 121,
    "student_kl": 0.045422,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.045422,
    "selection_score": 0.045422,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef most_frequent(xs):\n    \"\"\"Return the element that appears most often in the list ``xs``. If multiple elements tie for highest frequency, return the smallest such element. The list always has at least one element.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 65,
    "student_kl": 0.043212,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.043212,
    "selection_score": 0.043212,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 346,
    "student_kl": 0.277055,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.277055,
    "selection_score": 0.277055,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef digital_root(n):\n    \"\"\"Return the digital root of the non-negative integer ``n``: repeatedly sum the decimal digits until the result has a single digit.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 72,
    "student_kl": 0.216439,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.216439,
    "selection_score": 0.216439,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 223,
    "student_kl": 0.203227,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203227,
    "selection_score": 0.203227,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 258,
    "student_kl": 0.19671,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.19671,
    "selection_score": 0.19671,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 10]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 149,
    "student_kl": 0.187792,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.187792,
    "selection_score": 0.187792,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 10, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 184,
    "student_kl": 0.184268,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.184268,
    "selection_score": 0.184268,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef unique_paths(m, n):\n    \"\"\"Return the number of unique paths from the top-left corner to the bottom-right corner of an ``m \u00d7 n`` grid where you can only move right or down at each step. ``m`` and ``n`` are positive integers.\n\n    >>> unique_paths(2, 2)\n    2\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 99,
    "student_kl": 0.178823,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178823,
    "selection_score": 0.178823,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 163,
    "student_kl": 0.173955,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173955,
    "selection_score": 0.173955,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [2, 10, 20, 25]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 225,
    "student_kl": 0.164794,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.164794,
    "selection_score": 0.164794,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 2, 20]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 163,
    "student_kl": 0.144238,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.144238,
    "selection_score": 0.144238,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 5, 10]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 172,
    "student_kl": 0.139331,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.139331,
    "selection_score": 0.139331,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef repeat_chars(s):\n    \"\"\"Return a string where every character of ``s`` is repeated 4 times in place. ``repeat_chars('ab')`` is ``'aaaabbbb'``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.137616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.137616,
    "selection_score": 0.137616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef repeat_chars(s):\n    \"\"\"Return a string where every character of ``s`` is repeated 2 times in place. ``repeat_chars('ab')`` is ``'aabb'``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 13,
    "student_kl": 0.137001,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.137001,
    "selection_score": 0.137001,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [5, 25, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 143,
    "student_kl": 0.134708,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.134708,
    "selection_score": 0.134708,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_max_sum(xs, k):\n    \"\"\"Return the maximum sum of any contiguous window of exactly ``k`` consecutive elements in the list ``xs``. If ``k`` is larger than the length of ``xs`` or ``xs`` is empty, return 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 85,
    "student_kl": 0.12824,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.12824,
    "selection_score": 0.12824,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef aggregate(xs):\n    \"\"\"Return the product of the non-zero elements of ``xs``. If every element is zero, return 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 52,
    "student_kl": 0.124755,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.124755,
    "selection_score": 0.124755,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef is_anagram(a, b):\n    \"\"\"Return True if string ``a`` is an anagram of string ``b`` (case-sensitive). Different lengths return False.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 24,
    "student_kl": 0.116899,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.116899,
    "selection_score": 0.116899,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef min_coins(amount):\n    \"\"\"Return the minimum number of coins needed to make ``amount`` using denominations [1, 5, 10, 50]. ``amount`` is a non-negative integer.\n    Each denomination may be used any number of times. If ``amount`` cannot be made with these coins, return -1. ``min_coins(0)`` is 0.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 185,
    "student_kl": 0.104125,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.104125,
    "selection_score": 0.104125,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_min(xs):\n    \"\"\"Return a list of the minimums of every contiguous window of exactly 2 elements in ``xs``. If ``xs`` has fewer than 2 elements, return []. The output has length ``max(0, len(xs) - 2 + 1)``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 38,
    "student_kl": 0.103701,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.103701,
    "selection_score": 0.103701,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef compress(s):\n    \"\"\"Return a run-length-encoded version of ``s`` of the form 'a3b2c4' (character followed by run length, with run length=1 also written as 'a1'). If the encoded form is not strictly shorter than the original, return the original string instead. Empty input returns ''.\n\n    >>> compress('aaabbc')\n    'a3b2c1'\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 132,
    "student_kl": 0.103147,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.103147,
    "selection_score": 0.103147,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef is_balanced_multi(s):\n    \"\"\"Return True iff every opening bracket in ``s`` has a matching closing bracket of the same type and they are properly nested. The bracket types are '()', '[]', and '{}'. Other characters are ignored. Empty string is True.\n\n    >>> is_balanced_multi('([{}])')\n    True\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 72,
    "student_kl": 0.098944,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.098944,
    "selection_score": 0.098944,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef split_paren_groups(s):\n    \"\"\"The input is a string containing only '(' and ')' characters and spaces. The parentheses form one or more balanced groups concatenated (possibly separated by spaces, which should be ignored). Return a list of the balanced groups in order, with all spaces removed. Each output group is itself balanced. The empty input returns [].\n\n    >>> split_paren_groups('( ) (( ))')\n    ['()', '(())']\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 97,
    "student_kl": 0.096256,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.096256,
    "selection_score": 0.096256,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef window_min(xs):\n    \"\"\"Return a list of the minimums of every contiguous window of exactly 3 elements in ``xs``. If ``xs`` has fewer than 3 elements, return []. The output has length ``max(0, len(xs) - 3 + 1)``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 36,
    "student_kl": 0.0951,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.0951,
    "selection_score": 0.0951,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef two_sum_indices(xs):\n    \"\"\"Return a sorted list of all unordered pairs (i, j) with i < j such that ``xs[i] + xs[j] == 3``. Pairs are tuples. The output is sorted by (i, j). Empty result returns [].\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 39,
    "student_kl": 0.09439,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.09439,
    "selection_score": 0.09439,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef most_frequent(xs):\n    \"\"\"Return the element that appears most often in the list ``xs``. If multiple elements tie for highest frequency, return the smallest such element. The list always has at least one element.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 73,
    "student_kl": 0.093336,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.093336,
    "selection_score": 0.093336,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "code",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nComplete the following Python function. Output only the function body (no extra explanation, no markdown fences).\n\ndef aggregate(xs):\n    \"\"\"Return the number of strictly positive elements of ``xs``.\n    \"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 16,
    "student_kl": 0.091323,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.091323,
    "selection_score": 0.091323,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nPrayrtgust is planning a 5-night trip with 6 other people, but they're each paying their own way. Prayrtgust's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Prayrtgust's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 512,
    "student_kl": 0.340635,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.340635,
    "selection_score": 0.340635,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nChutmeeld is planning a 6-night trip with 6 other people, but they're each paying their own way. Chutmeeld's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $200. How many dollars will Chutmeeld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 512,
    "student_kl": 0.322011,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.322011,
    "selection_score": 0.322011,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nStasnayck is planning a 6-night trip with 2 other people, but they're each paying their own way. Stasnayck's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Stasnayck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 512,
    "student_kl": 0.321829,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.321829,
    "selection_score": 0.321829,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSpoungjayttieck is planning a 6-night trip with 6 other people, but they're each paying their own way. Spoungjayttieck's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Spoungjayttieck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 512,
    "student_kl": 0.321295,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.321295,
    "selection_score": 0.321295,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nVairdvayckwien is planning a 8-night trip with 2 other people, but they're each paying their own way. Vairdvayckwien's lodging costs $80 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Vairdvayckwien's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 512,
    "student_kl": 0.313183,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.313183,
    "selection_score": 0.313183,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nGieldthiert is planning a 6-night trip with 4 other people, but they're each paying their own way. Gieldthiert's lodging costs $120 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Gieldthiert's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 512,
    "student_kl": 0.304225,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.304225,
    "selection_score": 0.304225,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nPlietgrouldsoard is planning a 3-night trip with 2 other people, but they're each paying their own way. Plietgrouldsoard's lodging costs $80 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Plietgrouldsoard's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 512,
    "student_kl": 0.301995,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.301995,
    "selection_score": 0.301995,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Hurdfost runs a reading club. 8 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 4 books were returned late. The library charges $5 per late book. They also used the fines to buy 14 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 284,
    "student_kl": 0.292279,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.292279,
    "selection_score": 0.292279,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Stoaldshait runs a reading club. 17 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 5 books were returned late. The library charges $5 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 317,
    "student_kl": 0.287025,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.287025,
    "selection_score": 0.287025,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHainslurgloang is planning a 8-night trip with 2 other people, but they're each paying their own way. Hainslurgloang's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Hainslurgloang's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 512,
    "student_kl": 0.276396,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.276396,
    "selection_score": 0.276396,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nProursmotrot is planning a 3-night trip with 2 other people, but they're each paying their own way. Proursmotrot's lodging costs $150 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Proursmotrot's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 512,
    "student_kl": 0.266847,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.266847,
    "selection_score": 0.266847,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Mierbrack runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 6 books were returned late. The library charges $5 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 270,
    "student_kl": 0.266614,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.266614,
    "selection_score": 0.266614,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Drielsmir runs a reading club. 13 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 7 books were returned late. The library charges $2 per late book. They also used the fines to buy 14 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 410,
    "student_kl": 0.260141,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.260141,
    "selection_score": 0.260141,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCelaingcrayld is planning a 8-night trip with 2 other people, but they're each paying their own way. Celaingcrayld's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $120. How many dollars will Celaingcrayld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 512,
    "student_kl": 0.25898,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.25898,
    "selection_score": 0.25898,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRickjail is planning a 7-night trip with 6 other people, but they're each paying their own way. Rickjail's lodging costs $90 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Rickjail's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 512,
    "student_kl": 0.257431,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.257431,
    "selection_score": 0.257431,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Wayrflour runs a reading club. 10 members each borrowed 4 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 323,
    "student_kl": 0.254037,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.254037,
    "selection_score": 0.254037,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nZairtdrayld is planning a 5-night trip with 2 other people, but they're each paying their own way. Zairtdrayld's lodging costs $90 per night, meals cost $40 per day, and round-trip transport costs $150. How many dollars will Zairtdrayld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 512,
    "student_kl": 0.252373,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.252373,
    "selection_score": 0.252373,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Thieckmaycrield runs a reading club. 14 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 8 books were returned late. The library charges $2 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 482,
    "student_kl": 0.251899,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.251899,
    "selection_score": 0.251899,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSlatsle goes to the vilclisshop with $40. Their friend Wiespoal, who is 13 years old, comes along but doesn't buy anything. Slatsle buys 7 glirdspas at $7 each and 6 bouckkaings at $5 each. How many dollars does Slatsle have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 512,
    "student_kl": 0.249805,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.249805,
    "selection_score": 0.249805,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nVeesshiet is planning a 4-night trip with 4 other people, but they're each paying their own way. Veesshiet's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Veesshiet's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 462,
    "student_kl": 0.236085,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.236085,
    "selection_score": 0.236085,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Drayrbroust runs a reading club. 19 members each borrowed 3 books for the month. The library opens at 15:00 each day. By the deadline, 7 books were returned late. The library charges $3 per late book. They also used the fines to buy 6 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 231,
    "student_kl": 0.233736,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233736,
    "selection_score": 0.233736,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Tiecknoathald runs a reading club. 20 members each borrowed 4 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $5 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 289,
    "student_kl": 0.227522,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.227522,
    "selection_score": 0.227522,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Chitzayrt runs a reading club. 14 members each borrowed 3 books for the month. The library opens at 12:00 each day. By the deadline, 8 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 249,
    "student_kl": 0.226273,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.226273,
    "selection_score": 0.226273,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Snoastplierdswayr runs a reading club. 11 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 12 books were returned late. The library charges $3 per late book. They also used the fines to buy 13 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 269,
    "student_kl": 0.224744,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.224744,
    "selection_score": 0.224744,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Gienbaick runs a reading club. 10 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 6 books were returned late. The library charges $2 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 321,
    "student_kl": 0.223352,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223352,
    "selection_score": 0.223352,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nZeenbren is planning a 7-night trip with 6 other people, but they're each paying their own way. Zeenbren's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Zeenbren's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
    "student_kl": 0.221636,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.221636,
    "selection_score": 0.221636,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Zailddayt runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $2 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 257,
    "student_kl": 0.218929,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.218929,
    "selection_score": 0.218929,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSweazout is planning a 3-night trip with 6 other people, but they're each paying their own way. Sweazout's lodging costs $150 per night, meals cost $30 per day, and round-trip transport costs $80. How many dollars will Sweazout's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 512,
    "student_kl": 0.218775,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.218775,
    "selection_score": 0.218775,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Zildfleen is building 3 brick walls using a 8-foot ladder. Each wall needs 200 bricks. Zildfleen also orders 50 extra bricks as a safety margin. During delivery, 20 bricks arrive broken and have to be discarded. How many usable bricks does Zildfleen have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 311,
    "student_kl": 0.214823,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.214823,
    "selection_score": 0.214823,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nStiepeck is planning a 5-night trip with 6 other people, but they're each paying their own way. Stiepeck's lodging costs $60 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Stiepeck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 512,
    "student_kl": 0.21175,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.21175,
    "selection_score": 0.21175,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Speestlald runs a reading club. 9 members each borrowed 4 books for the month. The library opens at 12:00 each day. By the deadline, 10 books were returned late. The library charges $3 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 254,
    "student_kl": 0.211275,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.211275,
    "selection_score": 0.211275,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 06:05 on a 12-hour clock. It runs for 3 hours and 28 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 512,
    "student_kl": 0.211166,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.211166,
    "selection_score": 0.211166,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 07:57 on a 12-hour clock. It runs for 11 hours and 10 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 512,
    "student_kl": 0.208549,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.208549,
    "selection_score": 0.208549,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA shop has 1228 items in stock. They sell 40% of them on Monday, then receive 80 new items. How many items have left the shop, plus the new arrivals (i.e. 40% of 1228 plus 80)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 512,
    "student_kl": 0.208356,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.208356,
    "selection_score": 0.208356,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Tresnain runs a reading club. 20 members each borrowed 4 books for the month. The library opens at 12:00 each day. By the deadline, 4 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 243,
    "student_kl": 0.203483,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203483,
    "selection_score": 0.203483,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Priestzaylgrist is building 3 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Priestzaylgrist also orders 20 extra bricks as a safety margin. During delivery, 15 bricks arrive broken and have to be discarded. How many usable bricks does Priestzaylgrist have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 311,
    "student_kl": 0.202676,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.202676,
    "selection_score": 0.202676,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Bostglick runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 12 books were returned late. The library charges $3 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 261,
    "student_kl": 0.201494,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.201494,
    "selection_score": 0.201494,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Sniersmoald is building 5 brick walls using a 10-foot ladder. Each wall needs 150 bricks. Sniersmoald also orders 30 extra bricks as a safety margin. During delivery, 25 bricks arrive broken and have to be discarded. How many usable bricks does Sniersmoald have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 314,
    "student_kl": 0.199116,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.199116,
    "selection_score": 0.199116,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nTeastflist runs an orchard with 7 rows of apple trees. Each row has 11 trees, and each tree produces 25 apples this season. 10% of the apples are spoiled by frost, and Teastflist saves 186 apples for the farmer's market next weekend. How many apples are left for Teastflist to sell to the local grocer?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 512,
    "student_kl": 0.195245,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195245,
    "selection_score": 0.195245,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFockkeatgil is planning a 5-night trip with 6 other people, but they're each paying their own way. Fockkeatgil's lodging costs $60 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Fockkeatgil's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 512,
    "student_kl": 0.192214,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.192214,
    "selection_score": 0.192214,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Fangrientaing is building 4 brick walls using a 8-foot ladder. Each wall needs 150 bricks. Fangrientaing also orders 30 extra bricks as a safety margin. During delivery, 5 bricks arrive broken and have to be discarded. How many usable bricks does Fangrientaing have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 345,
    "student_kl": 0.190266,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190266,
    "selection_score": 0.190266,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nPlearttroart keeps 21 chickens in a 18-meter coop. Each chicken lays 7 eggs per week. Over 6 weeks, the family ate 12 eggs for breakfast and donated 6 eggs to a neighbor. How many eggs are left at the end of the 6 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 512,
    "student_kl": 0.189549,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189549,
    "selection_score": 0.189549,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 5 hours and 34 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 169,
    "student_kl": 0.189021,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189021,
    "selection_score": 0.189021,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Flearbrienjor is building 3 brick walls using a 12-foot ladder. Each wall needs 150 bricks. Flearbrienjor also orders 50 extra bricks as a safety margin. During delivery, 24 bricks arrive broken and have to be discarded. How many usable bricks does Flearbrienjor have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 287,
    "student_kl": 0.18809,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.18809,
    "selection_score": 0.18809,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nTeacher Gourfit runs an after-school program with 5 classes. Each class has 30 students enrolled, but on Monday 1 students in each class were absent. 3 parent volunteers also stayed to help. The school district has 7 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 232,
    "student_kl": 0.186948,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186948,
    "selection_score": 0.186948,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Raiskas is building 5 brick walls using a 8-foot ladder. Each wall needs 200 bricks. Raiskas also orders 50 extra bricks as a safety margin. During delivery, 22 bricks arrive broken and have to be discarded. How many usable bricks does Raiskas have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 401,
    "student_kl": 0.184428,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.184428,
    "selection_score": 0.184428,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA shop has 730 items in stock. They sell 12% of them on Monday, then receive 77 new items. How many items have left the shop, plus the new arrivals (i.e. 12% of 730 plus 77)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
    "student_kl": 0.183689,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.183689,
    "selection_score": 0.183689,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCaptain Boackning's basketball team played 9 games with 7 players on the field at any time. They won 6 games and lost 3 games. Each win is worth 2 league points, each loss is worth 0 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Boackning's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 330,
    "student_kl": 0.180739,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180739,
    "selection_score": 0.180739,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nBourtjiert keeps 9 chickens in a 18-meter coop. Each chicken lays 4 eggs per week. Over 2 weeks, the family ate 18 eggs for breakfast and donated 7 eggs to a neighbor. How many eggs are left at the end of the 2 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 295,
    "student_kl": 0.180195,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180195,
    "selection_score": 0.180195,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 8 servings and uses 2 cups of flour. Pleastbogray wants to make 16 servings for a school bake sale. They also need to add 4 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Pleastbogray need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 372,
    "student_kl": 0.179379,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179379,
    "selection_score": 0.179379,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nClesnan keeps 13 chickens in a 12-meter coop. Each chicken lays 6 eggs per week. Over 6 weeks, the family ate 12 eggs for breakfast and donated 15 eggs to a neighbor. How many eggs are left at the end of the 6 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
    "student_kl": 0.179376,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179376,
    "selection_score": 0.179376,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 12:23 on a 12-hour clock. It runs for 6 hours and 17 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 496,
    "student_kl": 0.17737,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17737,
    "selection_score": 0.17737,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nMestbayst goes to the theangskashouse with $50. Their friend Snoustchiest, who is 7 years old, comes along but doesn't buy anything. Mestbayst buys 8 neerboasts at $3 each and 3 zaitclengs at $9 each. How many dollars does Mestbayst have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 512,
    "student_kl": 0.176998,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176998,
    "selection_score": 0.176998,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Paswoaldsteeng is building 5 brick walls using a 10-foot ladder. Each wall needs 150 bricks. Paswoaldsteeng also orders 20 extra bricks as a safety margin. During delivery, 5 bricks arrive broken and have to be discarded. How many usable bricks does Paswoaldsteeng have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 289,
    "student_kl": 0.176269,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176269,
    "selection_score": 0.176269,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 01:26 on a 12-hour clock. It runs for 10 hours and 29 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 342,
    "student_kl": 0.176187,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176187,
    "selection_score": 0.176187,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Kistthaisjart is building 4 brick walls using a 12-foot ladder. Each wall needs 80 bricks. Kistthaisjart also orders 30 extra bricks as a safety margin. During delivery, 21 bricks arrive broken and have to be discarded. How many usable bricks does Kistthaisjart have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 275,
    "student_kl": 0.174423,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174423,
    "selection_score": 0.174423,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 9 hours and 55 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 192,
    "student_kl": 0.174357,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174357,
    "selection_score": 0.174357,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCelaingcrayld is planning a 8-night trip with 2 other people, but they're each paying their own way. Celaingcrayld's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $120. How many dollars will Celaingcrayld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 1024,
    "student_kl": 0.353222,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.353222,
    "selection_score": 0.353222,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSweazout is planning a 3-night trip with 6 other people, but they're each paying their own way. Sweazout's lodging costs $150 per night, meals cost $30 per day, and round-trip transport costs $80. How many dollars will Sweazout's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 1024,
    "student_kl": 0.324168,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.324168,
    "selection_score": 0.324168,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHainslurgloang is planning a 8-night trip with 2 other people, but they're each paying their own way. Hainslurgloang's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Hainslurgloang's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 1024,
    "student_kl": 0.312436,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.312436,
    "selection_score": 0.312436,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nStasnayck is planning a 6-night trip with 2 other people, but they're each paying their own way. Stasnayck's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Stasnayck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 1024,
    "student_kl": 0.304068,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.304068,
    "selection_score": 0.304068,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nVeesshiet is planning a 4-night trip with 4 other people, but they're each paying their own way. Veesshiet's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Veesshiet's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 1024,
    "student_kl": 0.293809,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.293809,
    "selection_score": 0.293809,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nVairdvayckwien is planning a 8-night trip with 2 other people, but they're each paying their own way. Vairdvayckwien's lodging costs $80 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Vairdvayckwien's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 1024,
    "student_kl": 0.292941,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.292941,
    "selection_score": 0.292941,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nProursmotrot is planning a 3-night trip with 2 other people, but they're each paying their own way. Proursmotrot's lodging costs $150 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Proursmotrot's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 1024,
    "student_kl": 0.290915,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.290915,
    "selection_score": 0.290915,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSpoungjayttieck is planning a 6-night trip with 6 other people, but they're each paying their own way. Spoungjayttieck's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Spoungjayttieck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 1024,
    "student_kl": 0.279784,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.279784,
    "selection_score": 0.279784,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Paswoaldsteeng is building 5 brick walls using a 10-foot ladder. Each wall needs 150 bricks. Paswoaldsteeng also orders 20 extra bricks as a safety margin. During delivery, 5 bricks arrive broken and have to be discarded. How many usable bricks does Paswoaldsteeng have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 1024,
    "student_kl": 0.274302,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.274302,
    "selection_score": 0.274302,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRickjail is planning a 7-night trip with 6 other people, but they're each paying their own way. Rickjail's lodging costs $90 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Rickjail's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 1024,
    "student_kl": 0.271073,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.271073,
    "selection_score": 0.271073,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Drielsmir runs a reading club. 13 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 7 books were returned late. The library charges $2 per late book. They also used the fines to buy 14 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 276,
    "student_kl": 0.268356,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.268356,
    "selection_score": 0.268356,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Stoaldshait runs a reading club. 17 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 5 books were returned late. The library charges $5 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 346,
    "student_kl": 0.267818,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.267818,
    "selection_score": 0.267818,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nGieldthiert is planning a 6-night trip with 4 other people, but they're each paying their own way. Gieldthiert's lodging costs $120 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Gieldthiert's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 1024,
    "student_kl": 0.264168,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.264168,
    "selection_score": 0.264168,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 01:26 on a 12-hour clock. It runs for 10 hours and 29 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 454,
    "student_kl": 0.261398,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.261398,
    "selection_score": 0.261398,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Zailddayt runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $2 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 236,
    "student_kl": 0.261159,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.261159,
    "selection_score": 0.261159,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Mierbrack runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 6 books were returned late. The library charges $5 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 247,
    "student_kl": 0.245283,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.245283,
    "selection_score": 0.245283,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Tresnain runs a reading club. 20 members each borrowed 4 books for the month. The library opens at 12:00 each day. By the deadline, 4 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 274,
    "student_kl": 0.243799,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.243799,
    "selection_score": 0.243799,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nZeenbren is planning a 7-night trip with 6 other people, but they're each paying their own way. Zeenbren's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Zeenbren's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 632,
    "student_kl": 0.243026,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.243026,
    "selection_score": 0.243026,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Thieckmaycrield runs a reading club. 14 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 8 books were returned late. The library charges $2 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 297,
    "student_kl": 0.242616,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.242616,
    "selection_score": 0.242616,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSwitfierd is planning a 4-night trip with 4 other people, but they're each paying their own way. Switfierd's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Switfierd's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 896,
    "student_kl": 0.24153,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.24153,
    "selection_score": 0.24153,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA shop has 730 items in stock. They sell 12% of them on Monday, then receive 77 new items. How many items have left the shop, plus the new arrivals (i.e. 12% of 730 plus 77)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 1024,
    "student_kl": 0.23768,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.23768,
    "selection_score": 0.23768,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Sniersmoald is building 5 brick walls using a 10-foot ladder. Each wall needs 150 bricks. Sniersmoald also orders 30 extra bricks as a safety margin. During delivery, 25 bricks arrive broken and have to be discarded. How many usable bricks does Sniersmoald have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 381,
    "student_kl": 0.234456,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.234456,
    "selection_score": 0.234456,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Hurdfost runs a reading club. 8 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 4 books were returned late. The library charges $5 per late book. They also used the fines to buy 14 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 332,
    "student_kl": 0.233406,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233406,
    "selection_score": 0.233406,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Gienbaick runs a reading club. 10 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 6 books were returned late. The library charges $2 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 321,
    "student_kl": 0.228449,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.228449,
    "selection_score": 0.228449,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Drayrbroust runs a reading club. 19 members each borrowed 3 books for the month. The library opens at 15:00 each day. By the deadline, 7 books were returned late. The library charges $3 per late book. They also used the fines to buy 6 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 266,
    "student_kl": 0.226102,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.226102,
    "selection_score": 0.226102,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nPlearttroart keeps 21 chickens in a 18-meter coop. Each chicken lays 7 eggs per week. Over 6 weeks, the family ate 12 eggs for breakfast and donated 6 eggs to a neighbor. How many eggs are left at the end of the 6 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 1024,
    "student_kl": 0.224534,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.224534,
    "selection_score": 0.224534,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Tiecknoathald runs a reading club. 20 members each borrowed 4 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $5 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 342,
    "student_kl": 0.222621,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.222621,
    "selection_score": 0.222621,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Chitzayrt runs a reading club. 14 members each borrowed 3 books for the month. The library opens at 12:00 each day. By the deadline, 8 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 242,
    "student_kl": 0.22215,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.22215,
    "selection_score": 0.22215,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Snoastplierdswayr runs a reading club. 11 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 12 books were returned late. The library charges $3 per late book. They also used the fines to buy 13 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 232,
    "student_kl": 0.221954,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.221954,
    "selection_score": 0.221954,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nZeenbren is planning a 7-night trip with 6 other people, but they're each paying their own way. Zeenbren's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Zeenbren's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 2048,
    "student_kl": 0.287963,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.287963,
    "selection_score": 0.287963,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHainslurgloang is planning a 8-night trip with 2 other people, but they're each paying their own way. Hainslurgloang's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Hainslurgloang's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 2048,
    "student_kl": 0.27918,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.27918,
    "selection_score": 0.27918,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nVeesshiet is planning a 4-night trip with 4 other people, but they're each paying their own way. Veesshiet's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Veesshiet's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 2048,
    "student_kl": 0.27214,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.27214,
    "selection_score": 0.27214,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Drielsmir runs a reading club. 13 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 7 books were returned late. The library charges $2 per late book. They also used the fines to buy 14 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 260,
    "student_kl": 0.267768,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.267768,
    "selection_score": 0.267768,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSlatsle goes to the vilclisshop with $40. Their friend Wiespoal, who is 13 years old, comes along but doesn't buy anything. Slatsle buys 7 glirdspas at $7 each and 6 bouckkaings at $5 each. How many dollars does Slatsle have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 1482,
    "student_kl": 0.261075,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.261075,
    "selection_score": 0.261075,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSwitfierd is planning a 4-night trip with 4 other people, but they're each paying their own way. Switfierd's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Switfierd's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 761,
    "student_kl": 0.258615,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.258615,
    "selection_score": 0.258615,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCelaingcrayld is planning a 8-night trip with 2 other people, but they're each paying their own way. Celaingcrayld's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $120. How many dollars will Celaingcrayld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 2048,
    "student_kl": 0.256632,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.256632,
    "selection_score": 0.256632,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nPlietgrouldsoard is planning a 3-night trip with 2 other people, but they're each paying their own way. Plietgrouldsoard's lodging costs $80 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Plietgrouldsoard's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 2048,
    "student_kl": 0.256147,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.256147,
    "selection_score": 0.256147,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Stoaldshait runs a reading club. 17 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 5 books were returned late. The library charges $5 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 328,
    "student_kl": 0.252406,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.252406,
    "selection_score": 0.252406,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nPrayrtgust is planning a 5-night trip with 6 other people, but they're each paying their own way. Prayrtgust's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Prayrtgust's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 2048,
    "student_kl": 0.251034,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.251034,
    "selection_score": 0.251034,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how the trade-off between flexibility and consistency in policy works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 512,
    "student_kl": 0.553611,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.553611,
    "selection_score": 0.553611,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how how curiosity functions as a self-reinforcing loop works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 505,
    "student_kl": 0.553078,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.553078,
    "selection_score": 0.553078,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how why retrospective analyses tend to outperform optimistic forecasts works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 512,
    "student_kl": 0.551036,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.551036,
    "selection_score": 0.551036,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of why second-order effects often matter more than first-order ones. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 512,
    "student_kl": 0.549698,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.549698,
    "selection_score": 0.549698,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on why second-order effects often matter more than first-order ones. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 512,
    "student_kl": 0.548293,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.548293,
    "selection_score": 0.548293,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how the role of constraints in driving creative output works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 512,
    "student_kl": 0.547912,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.547912,
    "selection_score": 0.547912,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCompose a 350-500 word essay arguing for or against why honest disagreement is often more useful than polite agreement. State your position clearly, give two supporting reasons in separate paragraphs, and acknowledge one counter-argument.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 512,
    "student_kl": 0.547756,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.547756,
    "selection_score": 0.547756,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on how peer review functions as a feedback mechanism. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 512,
    "student_kl": 0.538573,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.538573,
    "selection_score": 0.538573,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of how teams maintain reliability without slowing delivery. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 512,
    "student_kl": 0.531805,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.531805,
    "selection_score": 0.531805,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on how teams maintain reliability without slowing delivery. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 512,
    "student_kl": 0.527793,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.527793,
    "selection_score": 0.527793,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how how good naming conventions reduce cognitive load works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 512,
    "student_kl": 0.525136,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.525136,
    "selection_score": 0.525136,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of how curiosity functions as a self-reinforcing loop. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 508,
    "student_kl": 0.524325,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.524325,
    "selection_score": 0.524325,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how the difference between explanation and prediction in scientific work works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 512,
    "student_kl": 0.52094,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.52094,
    "selection_score": 0.52094,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCompose a 350-500 word essay arguing for or against the difference between memorisation and genuine understanding when learning a new skill. State your position clearly, give two supporting reasons in separate paragraphs, and acknowledge one counter-argument.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 512,
    "student_kl": 0.519724,
    "reference_kl": null,
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    "hardness_gap": 0.519724,
    "selection_score": 0.519724,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of why version control changed how software teams collaborate. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 425,
    "student_kl": 0.519356,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.519356,
    "selection_score": 0.519356,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of why measurement systems shape the behaviours they're meant to track. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 512,
    "student_kl": 0.518912,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.518912,
    "selection_score": 0.518912,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on why retrospective analyses tend to outperform optimistic forecasts. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 512,
    "student_kl": 0.518518,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.518518,
    "selection_score": 0.518518,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCompose a 350-500 word essay arguing for or against the trade-off between flexibility and consistency in policy. State your position clearly, give two supporting reasons in separate paragraphs, and acknowledge one counter-argument.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
    "student_kl": 0.509933,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.509933,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how the role of compounding effects in long-term planning works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 512,
    "student_kl": 0.509317,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.509317,
    "selection_score": 0.509317,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCompose a 350-500 word essay arguing for or against how peer review functions as a feedback mechanism. State your position clearly, give two supporting reasons in separate paragraphs, and acknowledge one counter-argument.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 512,
    "student_kl": 0.507121,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.507121,
    "selection_score": 0.507121,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCompose a 350-500 word essay arguing for or against the trade-off between simplicity and capability in software design. State your position clearly, give two supporting reasons in separate paragraphs, and acknowledge one counter-argument.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 512,
    "student_kl": 0.503705,
    "reference_kl": null,
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    "selection_mode": "self",
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    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of how peer review functions as a feedback mechanism. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 477,
    "student_kl": 0.502961,
    "reference_kl": null,
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    "hardness_gap": 0.502961,
    "selection_score": 0.502961,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nCompose a 350-500 word essay arguing for or against why second-order effects often matter more than first-order ones. State your position clearly, give two supporting reasons in separate paragraphs, and acknowledge one counter-argument.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 512,
    "student_kl": 0.500746,
    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how how peer review functions as a feedback mechanism works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 480,
    "student_kl": 0.495853,
    "reference_kl": null,
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    "hardness_gap": 0.495853,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nIn 300-450 words and 2-3 paragraphs, describe how the role of slack capacity in resilient systems works and why it matters. Use plain language and avoid jargon.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
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    "reference_kl": null,
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    "selection_mode": "self",
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    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of why honest disagreement is often more useful than polite agreement. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
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    "reference_kl": null,
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    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on the trade-off between flexibility and consistency in policy. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 512,
    "student_kl": 0.485234,
    "reference_kl": null,
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    "hardness_gap": 0.485234,
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    "selection_mode": "self",
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    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 300-500 word analysis of the difference between explanation and prediction in scientific work. Use 2-3 paragraphs and include a clear thesis, supporting reasoning, and a brief conclusion.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 512,
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    "reference_kl": null,
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    "hardness_gap": 0.462271,
    "selection_score": 0.462271,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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    "axis": "long_form",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWrite a 350-500 word advice piece on the difference between memorisation and genuine understanding when learning a new skill. Open with a clear statement of the situation, give two-three concrete steps in the body, and close with a short summary.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 512,
    "student_kl": 0.456862,
    "reference_kl": null,
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    "hardness_gap": 0.456862,
    "selection_score": 0.456862,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
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    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nStiepeck is planning a 5-night trip with 6 other people, but they're each paying their own way. Stiepeck's lodging costs $60 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Stiepeck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 2048,
    "student_kl": 0.249812,
    "reference_kl": null,
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    "hardness_gap": 0.249812,
    "selection_score": 0.249812,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Zailddayt runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $2 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 271,
    "student_kl": 0.248798,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.248798,
    "selection_score": 0.248798,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRickjail is planning a 7-night trip with 6 other people, but they're each paying their own way. Rickjail's lodging costs $90 per night, meals cost $20 per day, and round-trip transport costs $200. How many dollars will Rickjail's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 2048,
    "student_kl": 0.247367,
    "reference_kl": null,
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    "hardness_gap": 0.247367,
    "selection_score": 0.247367,
    "selection_mode": "self",
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    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToustflierd goes to the gertshesstall with $40. Their friend Haystthirt, who is 13 years old, comes along but doesn't buy anything. Toustflierd buys 8 braildcouns at $5 each and 2 foastjaists at $6 each. How many dollars does Toustflierd have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 2048,
    "student_kl": 0.24386,
    "reference_kl": null,
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    "hardness_gap": 0.24386,
    "selection_score": 0.24386,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nGieldthiert is planning a 6-night trip with 4 other people, but they're each paying their own way. Gieldthiert's lodging costs $120 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Gieldthiert's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 1569,
    "student_kl": 0.242076,
    "reference_kl": null,
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    "hardness_gap": 0.242076,
    "selection_score": 0.242076,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Thieckmaycrield runs a reading club. 14 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 8 books were returned late. The library charges $2 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 316,
    "student_kl": 0.233848,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233848,
    "selection_score": 0.233848,
    "selection_mode": "self",
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    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nFockkeatgil is planning a 5-night trip with 6 other people, but they're each paying their own way. Fockkeatgil's lodging costs $60 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Fockkeatgil's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 1385,
    "student_kl": 0.233224,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.233224,
    "selection_score": 0.233224,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Chitzayrt runs a reading club. 14 members each borrowed 3 books for the month. The library opens at 12:00 each day. By the deadline, 8 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 310,
    "student_kl": 0.232805,
    "reference_kl": null,
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    "hardness_gap": 0.232805,
    "selection_score": 0.232805,
    "selection_mode": "self",
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    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nVairdvayckwien is planning a 8-night trip with 2 other people, but they're each paying their own way. Vairdvayckwien's lodging costs $80 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Vairdvayckwien's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 2048,
    "student_kl": 0.22985,
    "reference_kl": null,
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    "hardness_gap": 0.22985,
    "selection_score": 0.22985,
    "selection_mode": "self",
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    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nChutmeeld is planning a 6-night trip with 6 other people, but they're each paying their own way. Chutmeeld's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $200. How many dollars will Chutmeeld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 2048,
    "student_kl": 0.226661,
    "reference_kl": null,
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    "hardness_gap": 0.226661,
    "selection_score": 0.226661,
    "selection_mode": "self",
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    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Speestlald runs a reading club. 9 members each borrowed 4 books for the month. The library opens at 12:00 each day. By the deadline, 10 books were returned late. The library charges $3 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 351,
    "student_kl": 0.224312,
    "reference_kl": null,
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    "hardness_gap": 0.224312,
    "selection_score": 0.224312,
    "selection_mode": "self",
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    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def sum_of_squares_swier(n):\n#     total = 0\n#     i = 1\n#     while i <= n:\n#         j = 0\n#         while j < 1:\n#             total = total + i * i\n#             j = j + 1\n#         i = i + 1\n#     return total\n#\n# Behaviour tests the refactor must pass:\n# assert candidate(3) == 14\n# assert candidate(5) == 55\n# assert candidate(1) == 1\n# assert candidate(0) == 0\n#\n# Now write the refactor below. Output only the function body.\ndef sum_of_squares_swier(n: int) -> int:\n    \"\"\"Return 1**2 + 2**2 + ... + n**2.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 14,
    "student_kl": 0.223433,
    "reference_kl": null,
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    "selection_score": 0.223433,
    "selection_mode": "self",
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    "selection_backfill": true
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    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Snoastplierdswayr runs a reading club. 11 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 12 books were returned late. The library charges $3 per late book. They also used the fines to buy 13 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 242,
    "student_kl": 0.223082,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.223082,
    "selection_score": 0.223082,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Tiecknoathald runs a reading club. 20 members each borrowed 4 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $5 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 251,
    "student_kl": 0.222442,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.222442,
    "selection_score": 0.222442,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Wayrflour runs a reading club. 10 members each borrowed 4 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 255,
    "student_kl": 0.221838,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.221838,
    "selection_score": 0.221838,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Gienbaick runs a reading club. 10 members each borrowed 2 books for the month. The library opens at 18:00 each day. By the deadline, 6 books were returned late. The library charges $2 per late book. They also used the fines to buy 7 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 306,
    "student_kl": 0.221525,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.221525,
    "selection_score": 0.221525,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_pield(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_pield(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 14,
    "student_kl": 0.220703,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.220703,
    "selection_score": 0.220703,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSpoungjayttieck is planning a 6-night trip with 6 other people, but they're each paying their own way. Spoungjayttieck's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Spoungjayttieck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 1582,
    "student_kl": 0.220331,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.220331,
    "selection_score": 0.220331,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Bostglick runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 12 books were returned late. The library charges $3 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 258,
    "student_kl": 0.220274,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.220274,
    "selection_score": 0.220274,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nPrayrtgust is planning a 5-night trip with 6 other people, but they're each paying their own way. Prayrtgust's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $80. How many dollars will Prayrtgust's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 1024,
    "student_kl": 0.219645,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219645,
    "selection_score": 0.219645,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_fild(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_fild(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 14,
    "student_kl": 0.219364,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.219364,
    "selection_score": 0.219364,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nChutmeeld is planning a 6-night trip with 6 other people, but they're each paying their own way. Chutmeeld's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $200. How many dollars will Chutmeeld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 1024,
    "student_kl": 0.218718,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.218718,
    "selection_score": 0.218718,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Poangsur is building 3 brick walls using a 8-foot ladder. Each wall needs 150 bricks. Poangsur also orders 50 extra bricks as a safety margin. During delivery, 12 bricks arrive broken and have to be discarded. How many usable bricks does Poangsur have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 297,
    "student_kl": 0.215924,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.215924,
    "selection_score": 0.215924,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Gloustsmea is building 6 brick walls using a 8-foot ladder. Each wall needs 100 bricks. Gloustsmea also orders 30 extra bricks as a safety margin. During delivery, 9 bricks arrive broken and have to be discarded. How many usable bricks does Gloustsmea have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 343,
    "student_kl": 0.21378,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.21378,
    "selection_score": 0.21378,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nZairtdrayld is planning a 5-night trip with 2 other people, but they're each paying their own way. Zairtdrayld's lodging costs $90 per night, meals cost $40 per day, and round-trip transport costs $150. How many dollars will Zairtdrayld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 2048,
    "student_kl": 0.21271,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.21271,
    "selection_score": 0.21271,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nTeastflist runs an orchard with 7 rows of apple trees. Each row has 11 trees, and each tree produces 25 apples this season. 10% of the apples are spoiled by frost, and Teastflist saves 186 apples for the farmer's market next weekend. How many apples are left for Teastflist to sell to the local grocer?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 2048,
    "student_kl": 0.212469,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.212469,
    "selection_score": 0.212469,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 8 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_trurt(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_trurt(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 14,
    "student_kl": 0.210471,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.210471,
    "selection_score": 0.210471,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Wayrflour runs a reading club. 10 members each borrowed 4 books for the month. The library opens at 18:00 each day. By the deadline, 11 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 261,
    "student_kl": 0.209857,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.209857,
    "selection_score": 0.209857,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_hourt(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_hourt(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 14,
    "student_kl": 0.209533,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.209533,
    "selection_score": 0.209533,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_dat(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_dat(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 31,
    "student_kl": 0.208553,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.208553,
    "selection_score": 0.208553,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nTeastflist runs an orchard with 7 rows of apple trees. Each row has 11 trees, and each tree produces 25 apples this season. 10% of the apples are spoiled by frost, and Teastflist saves 186 apples for the farmer's market next weekend. How many apples are left for Teastflist to sell to the local grocer?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 1024,
    "student_kl": 0.207073,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.207073,
    "selection_score": 0.207073,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Tresnain runs a reading club. 20 members each borrowed 4 books for the month. The library opens at 12:00 each day. By the deadline, 4 books were returned late. The library charges $5 per late book. They also used the fines to buy 12 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 315,
    "student_kl": 0.206914,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.206914,
    "selection_score": 0.206914,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Priestzaylgrist is building 3 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Priestzaylgrist also orders 20 extra bricks as a safety margin. During delivery, 15 bricks arrive broken and have to be discarded. How many usable bricks does Priestzaylgrist have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 314,
    "student_kl": 0.203582,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203582,
    "selection_score": 0.203582,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Drayrbroust runs a reading club. 19 members each borrowed 3 books for the month. The library opens at 15:00 each day. By the deadline, 7 books were returned late. The library charges $3 per late book. They also used the fines to buy 6 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 245,
    "student_kl": 0.203344,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203344,
    "selection_score": 0.203344,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 13 hours and 6 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 177,
    "student_kl": 0.203024,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.203024,
    "selection_score": 0.203024,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 7 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_flain(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_flain(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 14,
    "student_kl": 0.202912,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.202912,
    "selection_score": 0.202912,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nLibrarian Speestlald runs a reading club. 9 members each borrowed 4 books for the month. The library opens at 12:00 each day. By the deadline, 10 books were returned late. The library charges $3 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 242,
    "student_kl": 0.202312,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.202312,
    "selection_score": 0.202312,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nLibrarian Leerdflist runs a reading club. 17 members each borrowed 2 books for the month. The library opens at 15:00 each day. By the deadline, 10 books were returned late. The library charges $5 per late book. They also used the fines to buy 9 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 281,
    "student_kl": 0.2023,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.2023,
    "selection_score": 0.2023,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is May 10, 2024. Trayrbrild is 68 days old. What is the date 7 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 05/03/2024\n(B) 04/30/2024\n(C) 05/04/2024\n(D) 05/02/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 217,
    "student_kl": 0.201069,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.201069,
    "selection_score": 0.201069,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is September 9, 2023. Froudet is 38 days old. What is the date 41 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 07/30/2023\n(B) 07/27/2023\n(C) 07/29/2023\n(D) 07/31/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 512,
    "student_kl": 0.200893,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.200893,
    "selection_score": 0.200893,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nZairtdrayld is planning a 5-night trip with 2 other people, but they're each paying their own way. Zairtdrayld's lodging costs $90 per night, meals cost $40 per day, and round-trip transport costs $150. How many dollars will Zairtdrayld's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 728,
    "student_kl": 0.200066,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.200066,
    "selection_score": 0.200066,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFockkeatgil is planning a 5-night trip with 6 other people, but they're each paying their own way. Fockkeatgil's lodging costs $60 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Fockkeatgil's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 1024,
    "student_kl": 0.200059,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.200059,
    "selection_score": 0.200059,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is April 24, 2023. Smaytplas is 37 days old. What is the date 34 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 03/22/2023\n(B) 03/21/2023\n(C) 03/18/2023\n(D) 03/20/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 434,
    "student_kl": 0.200001,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.200001,
    "selection_score": 0.200001,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n((not False) and (not False)) and (not True)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 191,
    "student_kl": 0.199093,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.199093,
    "selection_score": 0.199093,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Hurdfost runs a reading club. 8 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 4 books were returned late. The library charges $5 per late book. They also used the fines to buy 14 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 248,
    "student_kl": 0.19907,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.19907,
    "selection_score": 0.19907,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must NOT use any explicit ``for`` or ``while`` loop. Use a comprehension, ``sum``, ``map``, ``any``, ``all``, or recursion instead.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_cries(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_cries(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 14,
    "student_kl": 0.198536,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.198536,
    "selection_score": 0.198536,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Raiskas is building 5 brick walls using a 8-foot ladder. Each wall needs 200 bricks. Raiskas also orders 50 extra bricks as a safety margin. During delivery, 22 bricks arrive broken and have to be discarded. How many usable bricks does Raiskas have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 281,
    "student_kl": 0.198202,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.198202,
    "selection_score": 0.198202,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:30 on a 12-hour clock. It runs for 4 hours and 15 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 512,
    "student_kl": 0.197739,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.197739,
    "selection_score": 0.197739,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSninbi ran a 3-hour charity fundraiser. 10 silver-tier donors gave $20 each. 7 gold-tier donors gave $50 each. A local company contributed an additional $200 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 245,
    "student_kl": 0.197484,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.197484,
    "selection_score": 0.197484,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nKoardchor keeps 12 chickens in a 18-meter coop. Each chicken lays 4 eggs per week. Over 5 weeks, the family ate 20 eggs for breakfast and donated 10 eggs to a neighbor. How many eggs are left at the end of the 5 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 307,
    "student_kl": 0.195835,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195835,
    "selection_score": 0.195835,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nProursmotrot is planning a 3-night trip with 2 other people, but they're each paying their own way. Proursmotrot's lodging costs $150 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Proursmotrot's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 2048,
    "student_kl": 0.195793,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195793,
    "selection_score": 0.195793,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Bostglick runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 12:00 each day. By the deadline, 12 books were returned late. The library charges $3 per late book. They also used the fines to buy 8 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 275,
    "student_kl": 0.195644,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195644,
    "selection_score": 0.195644,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Proardpreermeack is building 5 brick walls using a 12-foot ladder. Each wall needs 120 bricks. Proardpreermeack also orders 30 extra bricks as a safety margin. During delivery, 17 bricks arrive broken and have to be discarded. How many usable bricks does Proardpreermeack have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 383,
    "student_kl": 0.195307,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.195307,
    "selection_score": 0.195307,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nStiepeck is planning a 5-night trip with 6 other people, but they're each paying their own way. Stiepeck's lodging costs $60 per night, meals cost $30 per day, and round-trip transport costs $200. How many dollars will Stiepeck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 1024,
    "student_kl": 0.194774,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.194774,
    "selection_score": 0.194774,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 8-foot lamp at the origin (irrelevant). You turn around, then turn around, then turn around, then walk 2 steps forward, then turn right, then turn around. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 395,
    "student_kl": 0.194637,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.194637,
    "selection_score": 0.194637,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Gloustsmea is building 6 brick walls using a 8-foot ladder. Each wall needs 100 bricks. Gloustsmea also orders 30 extra bricks as a safety margin. During delivery, 9 bricks arrive broken and have to be discarded. How many usable bricks does Gloustsmea have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 369,
    "student_kl": 0.193749,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.193749,
    "selection_score": 0.193749,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA meeting starts at 07:57 on a 12-hour clock. It runs for 11 hours and 10 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 474,
    "student_kl": 0.193564,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.193564,
    "selection_score": 0.193564,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA meeting starts at 01:26 on a 12-hour clock. It runs for 10 hours and 29 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 411,
    "student_kl": 0.193435,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.193435,
    "selection_score": 0.193435,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Thiengjielgleat is building 6 brick walls using a 8-foot ladder. Each wall needs 120 bricks. Thiengjielgleat also orders 30 extra bricks as a safety margin. During delivery, 11 bricks arrive broken and have to be discarded. How many usable bricks does Thiengjielgleat have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 336,
    "student_kl": 0.193118,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.193118,
    "selection_score": 0.193118,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCaptain Flealnayrt's hockey team played 10 games with 7 players on the field at any time. They won 5 games and lost 5 games. Each win is worth 3 league points, each loss is worth 0 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Flealnayrt's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 337,
    "student_kl": 0.192988,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.192988,
    "selection_score": 0.192988,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is April 21, 2023. Chunskourd is 63 days old. What is the date 54 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 02/27/2023\n(B) 02/26/2023\n(C) 02/23/2023\n(D) 02/25/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 512,
    "student_kl": 0.192674,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.192674,
    "selection_score": 0.192674,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Choanthousjies is building 8 brick walls using a 8-foot ladder. Each wall needs 150 bricks. Choanthousjies also orders 20 extra bricks as a safety margin. During delivery, 10 bricks arrive broken and have to be discarded. How many usable bricks does Choanthousjies have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 319,
    "student_kl": 0.191694,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.191694,
    "selection_score": 0.191694,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSweazout is planning a 3-night trip with 6 other people, but they're each paying their own way. Sweazout's lodging costs $150 per night, meals cost $30 per day, and round-trip transport costs $80. How many dollars will Sweazout's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 1950,
    "student_kl": 0.191683,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.191683,
    "selection_score": 0.191683,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(not False) and (not False)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 146,
    "student_kl": 0.191639,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.191639,
    "selection_score": 0.191639,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nPlietgrouldsoard is planning a 3-night trip with 2 other people, but they're each paying their own way. Plietgrouldsoard's lodging costs $80 per night, meals cost $30 per day, and round-trip transport costs $150. How many dollars will Plietgrouldsoard's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 628,
    "student_kl": 0.190759,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190759,
    "selection_score": 0.190759,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nKaisttosmun lies. Kaisttosmun says Hockbrold tells the truth. Hockbrold says Tiestkursloal lies. A bystander mentions there are 8 people in the room (not relevant). Does Tiestkursloal tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 512,
    "student_kl": 0.190435,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190435,
    "selection_score": 0.190435,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nDraiflieck keeps 16 chickens in a 18-meter coop. Each chicken lays 7 eggs per week. Over 3 weeks, the family ate 12 eggs for breakfast and donated 10 eggs to a neighbor. How many eggs are left at the end of the 3 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 313,
    "student_kl": 0.19038,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.19038,
    "selection_score": 0.19038,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA shop has 582 items in stock. They sell 15% of them on Monday, then receive 20 new items. How many items have left the shop, plus the new arrivals (i.e. 15% of 582 plus 20)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 512,
    "student_kl": 0.190095,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.190095,
    "selection_score": 0.190095,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is November 9, 2023. Swulfeetcang is 65 days old. What is the date 62 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 09/05/2023\n(B) 09/08/2023\n(C) 09/07/2023\n(D) 09/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 512,
    "student_kl": 0.189795,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189795,
    "selection_score": 0.189795,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor body must be at most 6 non-blank, non-comment SOURCE LINES.\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_payng(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_payng(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 14,
    "student_kl": 0.189659,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.189659,
    "selection_score": 0.189659,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 07:28 on a 12-hour clock. It runs for 7 hours and 54 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 512,
    "student_kl": 0.187396,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.187396,
    "selection_score": 0.187396,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is September 25, 2023. Fliscroldfoul is 8 days old. What is the date 81 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 07/05/2023\n(B) 07/07/2023\n(C) 07/03/2023\n(D) 07/06/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 512,
    "student_kl": 0.187388,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.187388,
    "selection_score": 0.187388,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nLibrarian Mierbrack runs a reading club. 20 members each borrowed 5 books for the month. The library opens at 18:00 each day. By the deadline, 6 books were returned late. The library charges $5 per late book. They also used the fines to buy 15 replacement books later. How many dollars in late fees did the library collect?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 289,
    "student_kl": 0.187364,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.187364,
    "selection_score": 0.187364,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA pancakes recipe makes 6 servings and uses 5 cups of flour. Spourtcald wants to make 18 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Spourtcald need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 348,
    "student_kl": 0.187193,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.187193,
    "selection_score": 0.187193,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Fangrientaing is building 4 brick walls using a 8-foot ladder. Each wall needs 150 bricks. Fangrientaing also orders 30 extra bricks as a safety margin. During delivery, 5 bricks arrive broken and have to be discarded. How many usable bricks does Fangrientaing have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 338,
    "student_kl": 0.186842,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186842,
    "selection_score": 0.186842,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 6 servings and uses 5 cups of flour. Ploastnaingshais wants to make 12 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Ploastnaingshais need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 380,
    "student_kl": 0.186751,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186751,
    "selection_score": 0.186751,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is July 20, 2023. Boasttheel is 53 days old. What is the date 8 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 07/13/2023\n(B) 07/12/2023\n(C) 07/11/2023\n(D) 07/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 140,
    "student_kl": 0.186355,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186355,
    "selection_score": 0.186355,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is September 8, 2023. Snoarte is 17 days old. What is the date 68 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/12/2023\n(B) 11/14/2023\n(C) 11/16/2023\n(D) 11/15/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 362,
    "student_kl": 0.186181,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.186181,
    "selection_score": 0.186181,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Destfegeal is building 3 brick walls using a 8-foot ladder. Each wall needs 80 bricks. Destfegeal also orders 50 extra bricks as a safety margin. During delivery, 22 bricks arrive broken and have to be discarded. How many usable bricks does Destfegeal have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 320,
    "student_kl": 0.185462,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185462,
    "selection_score": 0.185462,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is November 18, 2023. Meengthar is 66 days old. What is the date 52 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 09/27/2023\n(B) 09/28/2023\n(C) 09/24/2023\n(D) 09/26/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 512,
    "student_kl": 0.185296,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185296,
    "selection_score": 0.185296,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA shop has 448 items in stock. They sell 40% of them on Monday, then receive 15 new items. How many items have left the shop, plus the new arrivals (i.e. 40% of 448 plus 15)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 512,
    "student_kl": 0.185286,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185286,
    "selection_score": 0.185286,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA meeting starts at 06:05 on a 12-hour clock. It runs for 3 hours and 28 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 442,
    "student_kl": 0.185199,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185199,
    "selection_score": 0.185199,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Pogil is building 8 brick walls using a 10-foot ladder. Each wall needs 80 bricks. Pogil also orders 50 extra bricks as a safety margin. During delivery, 8 bricks arrive broken and have to be discarded. How many usable bricks does Pogil have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 282,
    "student_kl": 0.185169,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185169,
    "selection_score": 0.185169,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSwelfleeldgrord keeps 11 chickens in a 12-meter coop. Each chicken lays 7 eggs per week. Over 4 weeks, the family ate 21 eggs for breakfast and donated 14 eggs to a neighbor. How many eggs are left at the end of the 4 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 310,
    "student_kl": 0.185013,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.185013,
    "selection_score": 0.185013,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 11-foot fence (irrelevant). You walk 5 steps forward, then walk 2 steps forward, then turn around. Which direction are you facing?\n\nOptions:\n(A) east\n(B) west\n(C) north\n(D) south<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 179,
    "student_kl": 0.184709,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.184709,
    "selection_score": 0.184709,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA shop has 1228 items in stock. They sell 40% of them on Monday, then receive 80 new items. How many items have left the shop, plus the new arrivals (i.e. 40% of 1228 plus 80)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 662,
    "student_kl": 0.184057,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.184057,
    "selection_score": 0.184057,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 8 hours and 20 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 185,
    "student_kl": 0.184025,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.184025,
    "selection_score": 0.184025,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:56 on a 12-hour clock. It runs for 6 hours and 46 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 508,
    "student_kl": 0.182821,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.182821,
    "selection_score": 0.182821,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 3-foot fence (irrelevant). You walk 5 steps forward, then walk 7 steps forward, then turn right, then walk 2 steps forward. Which direction are you facing?\n\nOptions:\n(A) east\n(B) south\n(C) north\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 231,
    "student_kl": 0.182351,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.182351,
    "selection_score": 0.182351,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nMestbayst goes to the theangskashouse with $50. Their friend Snoustchiest, who is 7 years old, comes along but doesn't buy anything. Mestbayst buys 8 neerboasts at $3 each and 3 zaitclengs at $9 each. How many dollars does Mestbayst have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 321,
    "student_kl": 0.182351,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.182351,
    "selection_score": 0.182351,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Laickshurdchayld is building 4 brick walls using a 8-foot ladder. Each wall needs 120 bricks. Laickshurdchayld also orders 30 extra bricks as a safety margin. During delivery, 17 bricks arrive broken and have to be discarded. How many usable bricks does Laickshurdchayld have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 296,
    "student_kl": 0.180857,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180857,
    "selection_score": 0.180857,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 6 servings and uses 5 cups of flour. Plirdswean wants to make 12 servings for a school bake sale. They also need to add 3 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Plirdswean need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 292,
    "student_kl": 0.180322,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180322,
    "selection_score": 0.180322,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 8 hours and 20 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 193,
    "student_kl": 0.180317,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.180317,
    "selection_score": 0.180317,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Heascoar's favorite colour is green.\n- Heascoar's favorite colour is not purple.\n- Sloackglurd's favorite colour is yellow.\n\nWhat is Heascoar's favorite colour?\n\nOptions:\n(A) yellow\n(B) purple\n(C) green<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 193,
    "student_kl": 0.18015,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.18015,
    "selection_score": 0.18015,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Baldgeld is building 3 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Baldgeld also orders 30 extra bricks as a safety margin. During delivery, 20 bricks arrive broken and have to be discarded. How many usable bricks does Baldgeld have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 241,
    "student_kl": 0.179818,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179818,
    "selection_score": 0.179818,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(True) or (True)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 150,
    "student_kl": 0.179658,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179658,
    "selection_score": 0.179658,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nKoaswourt tells the truth. Koaswourt says Pleestpeat lies. Pleestpeat says Spaldzaist lies. A bystander mentions there are 3 people in the room (not relevant). Does Spaldzaist tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 216,
    "student_kl": 0.179381,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.179381,
    "selection_score": 0.179381,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 7-foot fence (irrelevant). You turn left, then turn left, then turn right. Which direction are you facing?\n\nOptions:\n(A) east\n(B) north\n(C) west\n(D) south<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 139,
    "student_kl": 0.17893,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17893,
    "selection_score": 0.17893,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 10-foot lamp at the origin (irrelevant). You turn left, then walk 4 steps forward, then walk 3 steps forward. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 215,
    "student_kl": 0.178854,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178854,
    "selection_score": 0.178854,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA meeting starts at 12:23 on a 12-hour clock. It runs for 6 hours and 17 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 432,
    "student_kl": 0.178686,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178686,
    "selection_score": 0.178686,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nStartgleeld ran a 7-hour charity fundraiser. 8 silver-tier donors gave $25 each. 8 gold-tier donors gave $50 each. A local company contributed an additional $200 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 395,
    "student_kl": 0.17843,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17843,
    "selection_score": 0.17843,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 6-foot fence (irrelevant). You turn left, then turn left, then turn right, then turn right, then turn around. Which direction are you facing?\n\nOptions:\n(A) west\n(B) east\n(C) south\n(D) north<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 154,
    "student_kl": 0.178252,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178252,
    "selection_score": 0.178252,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 12:23 on a 12-hour clock. It runs for 6 hours and 17 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 688,
    "student_kl": 0.178051,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178051,
    "selection_score": 0.178051,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nBrulnoung keeps 9 chickens in a 18-meter coop. Each chicken lays 4 eggs per week. Over 3 weeks, the family ate 25 eggs for breakfast and donated 8 eggs to a neighbor. How many eggs are left at the end of the 3 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 305,
    "student_kl": 0.178014,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178014,
    "selection_score": 0.178014,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Geatslongriel is building 4 brick walls using a 10-foot ladder. Each wall needs 80 bricks. Geatslongriel also orders 50 extra bricks as a safety margin. During delivery, 25 bricks arrive broken and have to be discarded. How many usable bricks does Geatslongriel have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 326,
    "student_kl": 0.178009,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.178009,
    "selection_score": 0.178009,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n((not False) or (not True)) and (False)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 302,
    "student_kl": 0.177843,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.177843,
    "selection_score": 0.177843,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is July 22, 2024. Chalzain is 24 days old. What is the date 76 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 05/04/2024\n(B) 05/06/2024\n(C) 05/08/2024\n(D) 05/07/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 512,
    "student_kl": 0.177645,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.177645,
    "selection_score": 0.177645,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA shop has 730 items in stock. They sell 12% of them on Monday, then receive 77 new items. How many items have left the shop, plus the new arrivals (i.e. 12% of 730 plus 77)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 904,
    "student_kl": 0.17762,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17762,
    "selection_score": 0.17762,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 8 servings and uses 5 cups of flour. Hulourd wants to make 24 servings for a school bake sale. They also need to add 7 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Hulourd need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 353,
    "student_kl": 0.177406,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.177406,
    "selection_score": 0.177406,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nPrutreas ran a 7-hour charity fundraiser. 16 silver-tier donors gave $15 each. 8 gold-tier donors gave $75 each. A local company contributed an additional $300 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 311,
    "student_kl": 0.177347,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.177347,
    "selection_score": 0.177347,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nDesttheel keeps 12 chickens in a 12-meter coop. Each chicken lays 5 eggs per week. Over 3 weeks, the family ate 25 eggs for breakfast and donated 6 eggs to a neighbor. How many eggs are left at the end of the 3 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 305,
    "student_kl": 0.17729,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17729,
    "selection_score": 0.17729,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter G is to J as the letter O is to which letter?\n\nOptions:\n(A) Q\n(B) R\n(C) S\n(D) P<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 276,
    "student_kl": 0.176814,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176814,
    "selection_score": 0.176814,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 06:05 on a 12-hour clock. It runs for 3 hours and 28 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 297,
    "student_kl": 0.176722,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176722,
    "selection_score": 0.176722,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 8 servings and uses 2 cups of flour. Kuldveal wants to make 16 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 450 degrees, but that doesn't change the recipe. How many total cups of flour does Kuldveal need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 366,
    "student_kl": 0.176625,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176625,
    "selection_score": 0.176625,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is September 3, 2024. Sleeldflangrayn is 14 days old. What is the date 91 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 12/04/2024\n(B) 12/02/2024\n(C) 11/30/2024\n(D) 12/03/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 389,
    "student_kl": 0.176576,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176576,
    "selection_score": 0.176576,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is August 24, 2023. Gratskeal is 72 days old. What is the date 66 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 06/20/2023\n(B) 06/18/2023\n(C) 06/19/2023\n(D) 06/16/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 477,
    "student_kl": 0.176445,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176445,
    "selection_score": 0.176445,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is February 24, 2024. Woaldclaick is 68 days old. What is the date 77 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 12/08/2023\n(B) 12/06/2023\n(C) 12/10/2023\n(D) 12/09/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 512,
    "student_kl": 0.176205,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176205,
    "selection_score": 0.176205,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 5 hours and 34 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 191,
    "student_kl": 0.176095,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176095,
    "selection_score": 0.176095,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 8-foot fence (irrelevant). You turn around, then turn left, then walk 5 steps forward, then walk 2 steps forward, then turn right, then turn left. Which direction are you facing?\n\nOptions:\n(A) east\n(B) south\n(C) north\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 168,
    "student_kl": 0.176004,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.176004,
    "selection_score": 0.176004,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is December 22, 2023. Prourneatheel is 12 days old. What is the date 46 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/06/2023\n(B) 11/07/2023\n(C) 11/03/2023\n(D) 11/05/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 414,
    "student_kl": 0.175975,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175975,
    "selection_score": 0.175975,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Greessairtfleerd's basketball team played 9 games with 7 players on the field at any time. They won 5 games and lost 4 games. Each win is worth 2 league points, each loss is worth 0 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Greessairtfleerd's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 340,
    "student_kl": 0.175962,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175962,
    "selection_score": 0.175962,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nMestbayst goes to the theangskashouse with $50. Their friend Snoustchiest, who is 7 years old, comes along but doesn't buy anything. Mestbayst buys 8 neerboasts at $3 each and 3 zaitclengs at $9 each. How many dollars does Mestbayst have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 279,
    "student_kl": 0.175863,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175863,
    "selection_score": 0.175863,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter G is to H as the letter P is to which letter?\n\nOptions:\n(A) T\n(B) S\n(C) Q\n(D) O<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 236,
    "student_kl": 0.175748,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.175748,
    "selection_score": 0.175748,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is April 10, 2024. Cleertford is 31 days old. What is the date 13 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/22/2024\n(B) 04/20/2024\n(C) 04/24/2024\n(D) 04/23/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 273,
    "student_kl": 0.17504,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17504,
    "selection_score": 0.17504,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(False) or (False)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 127,
    "student_kl": 0.174947,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174947,
    "selection_score": 0.174947,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 9-foot lamp at the origin (irrelevant). You turn around, then turn around, then turn left, then walk 5 steps forward, then walk 1 steps forward, then turn around. Are you back at the starting point?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 365,
    "student_kl": 0.174912,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174912,
    "selection_score": 0.174912,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 9 hours and 55 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 195,
    "student_kl": 0.174878,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174878,
    "selection_score": 0.174878,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 4 servings and uses 5 cups of flour. Penskoat wants to make 12 servings for a school bake sale. They also need to add 4 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Penskoat need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 347,
    "student_kl": 0.174363,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174363,
    "selection_score": 0.174363,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Zildfleen is building 3 brick walls using a 8-foot ladder. Each wall needs 200 bricks. Zildfleen also orders 50 extra bricks as a safety margin. During delivery, 20 bricks arrive broken and have to be discarded. How many usable bricks does Zildfleen have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 337,
    "student_kl": 0.174267,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174267,
    "selection_score": 0.174267,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 10 hours and 19 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 192,
    "student_kl": 0.174237,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.174237,
    "selection_score": 0.174237,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 9 hours and 55 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 191,
    "student_kl": 0.17404,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17404,
    "selection_score": 0.17404,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(False) or (not False)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 158,
    "student_kl": 0.173948,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173948,
    "selection_score": 0.173948,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is March 20, 2024. Clongcissloart is 44 days old. What is the date 8 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 03/28/2024\n(B) 03/27/2024\n(C) 03/29/2024\n(D) 03/25/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 300,
    "student_kl": 0.173924,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173924,
    "selection_score": 0.173924,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nShatglielfoat lies. Shatglielfoat says Haistraingnoang lies. Haistraingnoang says Poarsustrirt tells the truth. Poarsustrirt says Rouckleenlain tells the truth. A bystander mentions there are 2 people in the room (not relevant). Does Rouckleenlain tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 512,
    "student_kl": 0.173756,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173756,
    "selection_score": 0.173756,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 8-foot fence (irrelevant). You turn right, then turn right, then turn left, then turn around. Which direction are you facing?\n\nOptions:\n(A) south\n(B) north\n(C) east\n(D) west<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 136,
    "student_kl": 0.173619,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173619,
    "selection_score": 0.173619,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 3 hours and 21 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 194,
    "student_kl": 0.173411,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173411,
    "selection_score": 0.173411,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA pancakes recipe makes 6 servings and uses 2 cups of flour. Skourdmoardcrit wants to make 18 servings for a school bake sale. They also need to add 3 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Skourdmoardcrit need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 372,
    "student_kl": 0.173106,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.173106,
    "selection_score": 0.173106,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA pancakes recipe makes 6 servings and uses 5 cups of flour. Spourtcald wants to make 18 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Spourtcald need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 373,
    "student_kl": 0.172849,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172849,
    "selection_score": 0.172849,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nTayrtroshit keeps 9 chickens in a 15-meter coop. Each chicken lays 7 eggs per week. Over 2 weeks, the family ate 10 eggs for breakfast and donated 13 eggs to a neighbor. How many eggs are left at the end of the 2 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 301,
    "student_kl": 0.172751,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172751,
    "selection_score": 0.172751,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nFouglou goes to the zaylsouckstall with $60. Their friend Jingratzoan, who is 11 years old, comes along but doesn't buy anything. Fouglou buys 5 sotberts at $5 each and 2 pangsnis at $10 each. How many dollars does Fouglou have left after the visit?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 247,
    "student_kl": 0.172696,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172696,
    "selection_score": 0.172696,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 8 servings and uses 5 cups of flour. Fayrdgreas wants to make 32 servings for a school bake sale. They also need to add 5 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Fayrdgreas need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 411,
    "student_kl": 0.172143,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172143,
    "selection_score": 0.172143,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Thuckvouldploan's favorite colour is purple.\n- Slutspaird's favorite colour is yellow.\n- Thuckvouldploan's favorite colour is not blue.\n\nWhat is Thuckvouldploan's favorite colour?\n\nOptions:\n(A) blue\n(B) purple\n(C) yellow<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 220,
    "student_kl": 0.172124,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172124,
    "selection_score": 0.172124,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 12 servings and uses 2 cups of flour. Prayfaitgies wants to make 36 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Prayfaitgies need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 337,
    "student_kl": 0.172016,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.172016,
    "selection_score": 0.172016,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA biscuits recipe makes 8 servings and uses 3 cups of flour. Brorttreal wants to make 24 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Brorttreal need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 369,
    "student_kl": 0.17195,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.17195,
    "selection_score": 0.17195,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nTeacher Bortsea runs an after-school program with 6 classes. Each class has 22 students enrolled, but on Monday 2 students in each class were absent. 5 parent volunteers also stayed to help. The school district has 7 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 232,
    "student_kl": 0.171943,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.171943,
    "selection_score": 0.171943,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Baldgeld is building 3 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Baldgeld also orders 30 extra bricks as a safety margin. During delivery, 20 bricks arrive broken and have to be discarded. How many usable bricks does Baldgeld have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 326,
    "student_kl": 0.171789,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.171789,
    "selection_score": 0.171789,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA shop has 1228 items in stock. They sell 40% of them on Monday, then receive 80 new items. How many items have left the shop, plus the new arrivals (i.e. 40% of 1228 plus 80)?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 350,
    "student_kl": 0.171464,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.171464,
    "selection_score": 0.171464,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Flearbrienjor is building 3 brick walls using a 12-foot ladder. Each wall needs 150 bricks. Flearbrienjor also orders 50 extra bricks as a safety margin. During delivery, 24 bricks arrive broken and have to be discarded. How many usable bricks does Flearbrienjor have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 301,
    "student_kl": 0.171086,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.171086,
    "selection_score": 0.171086,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 6 servings and uses 2 cups of flour. Jengflayrrain wants to make 12 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Jengflayrrain need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 393,
    "student_kl": 0.170971,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170971,
    "selection_score": 0.170971,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nSninbi ran a 3-hour charity fundraiser. 10 silver-tier donors gave $20 each. 7 gold-tier donors gave $50 each. A local company contributed an additional $200 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 236,
    "student_kl": 0.170882,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170882,
    "selection_score": 0.170882,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSmiestflourmayrt lies. Smiestflourmayrt says Foaskoas tells the truth. Foaskoas says Zelflous tells the truth. A bystander mentions there are 8 people in the room (not relevant). Does Zelflous tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100020,
    "continuation_tokens": 281,
    "student_kl": 0.170748,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170748,
    "selection_score": 0.170748,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_culd(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_culd(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 31,
    "student_kl": 0.170331,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170331,
    "selection_score": 0.170331,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nStasnayck is planning a 6-night trip with 2 other people, but they're each paying their own way. Stasnayck's lodging costs $120 per night, meals cost $20 per day, and round-trip transport costs $120. How many dollars will Stasnayck's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 432,
    "student_kl": 0.170224,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170224,
    "selection_score": 0.170224,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nRickplou keeps 8 chickens in a 18-meter coop. Each chicken lays 5 eggs per week. Over 5 weeks, the family ate 17 eggs for breakfast and donated 17 eggs to a neighbor. How many eggs are left at the end of the 5 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 315,
    "student_kl": 0.170021,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170021,
    "selection_score": 0.170021,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nContractor Choanthousjies is building 8 brick walls using a 8-foot ladder. Each wall needs 150 bricks. Choanthousjies also orders 20 extra bricks as a safety margin. During delivery, 10 bricks arrive broken and have to be discarded. How many usable bricks does Choanthousjies have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 376,
    "student_kl": 0.170011,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.170011,
    "selection_score": 0.170011,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nJeerkeart keeps 15 chickens in a 12-meter coop. Each chicken lays 7 eggs per week. Over 2 weeks, the family ate 20 eggs for breakfast and donated 15 eggs to a neighbor. How many eggs are left at the end of the 2 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 316,
    "student_kl": 0.169943,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169943,
    "selection_score": 0.169943,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 4 servings and uses 5 cups of flour. Penskoat wants to make 12 servings for a school bake sale. They also need to add 4 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Penskoat need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 375,
    "student_kl": 0.169928,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169928,
    "selection_score": 0.169928,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Prurtshorkes's basketball team played 17 games with 7 players on the field at any time. They won 9 games and lost 8 games. Each win is worth 2 league points, each loss is worth 1 consolation points, and the team got an extra 4 bonus points for fair play. How many total league points did Prurtshorkes's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 369,
    "student_kl": 0.169885,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169885,
    "selection_score": 0.169885,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Sniersmoald is building 5 brick walls using a 10-foot ladder. Each wall needs 150 bricks. Sniersmoald also orders 30 extra bricks as a safety margin. During delivery, 25 bricks arrive broken and have to be discarded. How many usable bricks does Sniersmoald have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 292,
    "student_kl": 0.169752,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169752,
    "selection_score": 0.169752,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 8 servings and uses 2 cups of flour. Pleastbogray wants to make 16 servings for a school bake sale. They also need to add 4 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Pleastbogray need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 329,
    "student_kl": 0.169731,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169731,
    "selection_score": 0.169731,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 3 hours and 21 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 191,
    "student_kl": 0.169713,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169713,
    "selection_score": 0.169713,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nClesnan keeps 13 chickens in a 12-meter coop. Each chicken lays 6 eggs per week. Over 6 weeks, the family ate 12 eggs for breakfast and donated 15 eggs to a neighbor. How many eggs are left at the end of the 6 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 313,
    "student_kl": 0.169646,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169646,
    "selection_score": 0.169646,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCouldtheslair keeps 8 chickens in a 12-meter coop. Each chicken lays 5 eggs per week. Over 4 weeks, the family ate 18 eggs for breakfast and donated 15 eggs to a neighbor. How many eggs are left at the end of the 4 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 271,
    "student_kl": 0.169601,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169601,
    "selection_score": 0.169601,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 11 hours and 43 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 196,
    "student_kl": 0.169275,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169275,
    "selection_score": 0.169275,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nTeacher Slaldrortvol runs an after-school program with 6 classes. Each class has 18 students enrolled, but on Monday 2 students in each class were absent. 5 parent volunteers also stayed to help. The school district has 9 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 243,
    "student_kl": 0.169105,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.169105,
    "selection_score": 0.169105,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Geatslongriel is building 4 brick walls using a 10-foot ladder. Each wall needs 80 bricks. Geatslongriel also orders 50 extra bricks as a safety margin. During delivery, 25 bricks arrive broken and have to be discarded. How many usable bricks does Geatslongriel have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 320,
    "student_kl": 0.168822,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168822,
    "selection_score": 0.168822,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nKoardchor keeps 12 chickens in a 18-meter coop. Each chicken lays 4 eggs per week. Over 5 weeks, the family ate 20 eggs for breakfast and donated 10 eggs to a neighbor. How many eggs are left at the end of the 5 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 304,
    "student_kl": 0.168737,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168737,
    "selection_score": 0.168737,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRickplou keeps 8 chickens in a 18-meter coop. Each chicken lays 5 eggs per week. Over 5 weeks, the family ate 17 eggs for breakfast and donated 17 eggs to a neighbor. How many eggs are left at the end of the 5 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 310,
    "student_kl": 0.168729,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168729,
    "selection_score": 0.168729,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 11 hours and 43 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 196,
    "student_kl": 0.16866,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16866,
    "selection_score": 0.16866,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nGreercli keeps 8 chickens in a 15-meter coop. Each chicken lays 5 eggs per week. Over 3 weeks, the family ate 18 eggs for breakfast and donated 9 eggs to a neighbor. How many eggs are left at the end of the 3 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 310,
    "student_kl": 0.168639,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168639,
    "selection_score": 0.168639,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nGreercli keeps 8 chickens in a 15-meter coop. Each chicken lays 5 eggs per week. Over 3 weeks, the family ate 18 eggs for breakfast and donated 9 eggs to a neighbor. How many eggs are left at the end of the 3 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 299,
    "student_kl": 0.16841,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16841,
    "selection_score": 0.16841,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is April 9, 2024. Frourdtis is 73 days old. What is the date 16 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 04/26/2024\n(B) 04/24/2024\n(C) 04/22/2024\n(D) 04/25/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 209,
    "student_kl": 0.168386,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168386,
    "selection_score": 0.168386,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA biscuits recipe makes 6 servings and uses 2 cups of flour. Mulsus wants to make 24 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Mulsus need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 501,
    "student_kl": 0.168074,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.168074,
    "selection_score": 0.168074,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSkinplin lies. Skinplin says Zeardrurt tells the truth. Zeardrurt says Floungtrart lies. Floungtrart says Thildshourt lies. Thildshourt says Creelddous lies. A bystander mentions there are 7 people in the room (not relevant). Does Creelddous tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 1024,
    "student_kl": 0.167844,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167844,
    "selection_score": 0.167844,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA biscuits recipe makes 8 servings and uses 5 cups of flour. Baildsleartswor wants to make 16 servings for a school bake sale. They also need to add 3 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Baildsleartswor need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 399,
    "student_kl": 0.167817,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167817,
    "selection_score": 0.167817,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA pancakes recipe makes 6 servings and uses 5 cups of flour. Spourtcald wants to make 18 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Spourtcald need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 377,
    "student_kl": 0.167755,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167755,
    "selection_score": 0.167755,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nTaickbostgiel keeps 25 chickens in a 12-meter coop. Each chicken lays 6 eggs per week. Over 4 weeks, the family ate 21 eggs for breakfast and donated 12 eggs to a neighbor. How many eggs are left at the end of the 4 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 314,
    "student_kl": 0.16775,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16775,
    "selection_score": 0.16775,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 12 servings and uses 2 cups of flour. Prayfaitgies wants to make 36 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Prayfaitgies need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 333,
    "student_kl": 0.167675,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167675,
    "selection_score": 0.167675,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nTeacher Zarfus runs an after-school program with 4 classes. Each class has 18 students enrolled, but on Monday 2 students in each class were absent. 4 parent volunteers also stayed to help. The school district has 9 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 230,
    "student_kl": 0.167576,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167576,
    "selection_score": 0.167576,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 6 servings and uses 3 cups of flour. Tacksnayt wants to make 12 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Tacksnayt need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 361,
    "student_kl": 0.167559,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167559,
    "selection_score": 0.167559,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is September 24, 2024. Kingfri is 13 days old. What is the date 57 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 11/17/2024\n(B) 11/20/2024\n(C) 11/19/2024\n(D) 11/21/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 986,
    "student_kl": 0.167432,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167432,
    "selection_score": 0.167432,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 4 servings and uses 5 cups of flour. Penskoat wants to make 12 servings for a school bake sale. They also need to add 4 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Penskoat need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 388,
    "student_kl": 0.167339,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167339,
    "selection_score": 0.167339,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nSnayrtcrot lies. Snayrtcrot says Doushoar lies. Doushoar says Thockveert lies. Thockveert says Smieldfree lies. A bystander mentions there are 7 people in the room (not relevant). Does Smieldfree tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 394,
    "student_kl": 0.167315,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167315,
    "selection_score": 0.167315,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is August 4, 2023. Dongrai is 58 days old. What is the date 40 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 09/10/2023\n(B) 09/13/2023\n(C) 09/14/2023\n(D) 09/12/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 343,
    "student_kl": 0.167241,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167241,
    "selection_score": 0.167241,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "refactor",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nRefactor the function shown. Your refactor must preserve behaviour AND meet the style constraint. Output only the function (signature + body), no extra explanation.\n\n# Refactor the following Python function. The reference\n# implementation below is correct but stylistically poor.\n# Your refactor must preserve EXACT behaviour (same inputs\n# return same outputs) AND satisfy the style constraint.\n#\n# Style constraint:\n# The refactor must contain NO loop nested inside another loop (no for-inside-for, no while-inside-while, no for-inside-while, no while-inside-for).\n#\n# Reference (poor style \u2014 DO NOT include in your output):\n# def flatten_two_level_spick(matrix):\n#     out = []\n#     for row in matrix:\n#         for x in row:\n#             out.append(x)\n#     return out\n#\n# Behaviour tests the refactor must pass:\n# assert candidate([[1, 2], [3, 4]]) == [1, 2, 3, 4]\n# assert candidate([[5]]) == [5]\n# assert candidate([]) == []\n# assert candidate([[1], [2], [3]]) == [1, 2, 3]\n#\n# Now write the refactor below. Output only the function body.\ndef flatten_two_level_spick(matrix: list[list[int]]) -> list[int]:\n    \"\"\"Flatten a 2D list of integers into a flat list.\"\"\"<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 31,
    "student_kl": 0.167127,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167127,
    "selection_score": 0.167127,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 3 hours and 21 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 193,
    "student_kl": 0.167077,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167077,
    "selection_score": 0.167077,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 12 servings and uses 5 cups of flour. Stourdholdbron wants to make 24 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 450 degrees, but that doesn't change the recipe. How many total cups of flour does Stourdholdbron need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 368,
    "student_kl": 0.167069,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167069,
    "selection_score": 0.167069,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 13 hours and 6 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100004,
    "continuation_tokens": 191,
    "student_kl": 0.167034,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.167034,
    "selection_score": 0.167034,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA biscuits recipe makes 12 servings and uses 2 cups of flour. Stuckthayld wants to make 48 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 450 degrees, but that doesn't change the recipe. How many total cups of flour does Stuckthayld need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 374,
    "student_kl": 0.166834,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.166834,
    "selection_score": 0.166834,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 10 hours and 19 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 197,
    "student_kl": 0.166585,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.166585,
    "selection_score": 0.166585,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nClesnan keeps 13 chickens in a 12-meter coop. Each chicken lays 6 eggs per week. Over 6 weeks, the family ate 12 eggs for breakfast and donated 15 eggs to a neighbor. How many eggs are left at the end of the 6 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 338,
    "student_kl": 0.166326,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.166326,
    "selection_score": 0.166326,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 10 hours and 19 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 188,
    "student_kl": 0.1663,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.1663,
    "selection_score": 0.1663,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 11 hours and 43 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 195,
    "student_kl": 0.166087,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.166087,
    "selection_score": 0.166087,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA meeting starts at 07:57 on a 12-hour clock. It runs for 11 hours and 10 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 825,
    "student_kl": 0.165896,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165896,
    "selection_score": 0.165896,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nDrardrat tells the truth. Drardrat says Hanvayncrart tells the truth. Hanvayncrart says Gleangnayng tells the truth. A bystander mentions there are 8 people in the room (not relevant). Does Gleangnayng tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 275,
    "student_kl": 0.165842,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165842,
    "selection_score": 0.165842,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing north. There is a 10-foot lamp at the origin (irrelevant). You turn right, then turn left, then walk 3 steps forward, then walk 7 steps forward. Are you back at the starting point?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 228,
    "student_kl": 0.165673,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165673,
    "selection_score": 0.165673,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:56 on a 12-hour clock. It runs for 6 hours and 46 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 393,
    "student_kl": 0.165629,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165629,
    "selection_score": 0.165629,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSwitfierd is planning a 4-night trip with 4 other people, but they're each paying their own way. Switfierd's lodging costs $60 per night, meals cost $20 per day, and round-trip transport costs $150. How many dollars will Switfierd's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 416,
    "student_kl": 0.165608,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165608,
    "selection_score": 0.165608,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 12 servings and uses 2 cups of flour. Prayfaitgies wants to make 36 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Prayfaitgies need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 368,
    "student_kl": 0.165171,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165171,
    "selection_score": 0.165171,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is November 18, 2023. Meengthar is 66 days old. What is the date 52 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 09/27/2023\n(B) 09/28/2023\n(C) 09/24/2023\n(D) 09/26/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100016,
    "continuation_tokens": 454,
    "student_kl": 0.16517,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16517,
    "selection_score": 0.16517,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Gloartpreartzes's rugby team played 17 games with 6 players on the field at any time. They won 13 games and lost 4 games. Each win is worth 3 league points, each loss is worth 0 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Gloartpreartzes's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 318,
    "student_kl": 0.165068,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165068,
    "selection_score": 0.165068,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nChortdiestpru lies. Chortdiestpru says Kaingbeack lies. Kaingbeack says Turtlolspurt tells the truth. Turtlolspurt says Lieldsmoasclord tells the truth. Lieldsmoasclord says Snielayng tells the truth. A bystander mentions there are 7 people in the room (not relevant). Does Snielayng tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 1024,
    "student_kl": 0.165057,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.165057,
    "selection_score": 0.165057,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 13-foot fence (irrelevant). You walk 5 steps forward, then turn around, then turn right, then turn left, then turn left, then turn right. Which direction are you facing?\n\nOptions:\n(A) north\n(B) west\n(C) east\n(D) south<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 343,
    "student_kl": 0.164968,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.164968,
    "selection_score": 0.164968,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Flealnayrt's hockey team played 10 games with 7 players on the field at any time. They won 5 games and lost 5 games. Each win is worth 3 league points, each loss is worth 0 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Flealnayrt's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 383,
    "student_kl": 0.164968,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.164968,
    "selection_score": 0.164968,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThe letter B is to I as the letter P is to which letter?\n\nOptions:\n(A) U\n(B) X\n(C) Z\n(D) W<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 313,
    "student_kl": 0.164744,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.164744,
    "selection_score": 0.164744,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing west. There is a 8-foot fence (irrelevant). You turn around, then walk 7 steps forward, then turn around, then walk 6 steps forward. Which direction are you facing?\n\nOptions:\n(A) south\n(B) west\n(C) north\n(D) east<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100003,
    "continuation_tokens": 190,
    "student_kl": 0.16431,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16431,
    "selection_score": 0.16431,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 8 hours and 20 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100006,
    "continuation_tokens": 195,
    "student_kl": 0.164225,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.164225,
    "selection_score": 0.164225,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nHow many total minutes are in 5 hours and 34 minutes?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100008,
    "continuation_tokens": 199,
    "student_kl": 0.164185,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.164185,
    "selection_score": 0.164185,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing east. There is a 5-foot fence (irrelevant). You turn left, then turn right, then turn left, then walk 5 steps forward, then turn right. Which direction are you facing?\n\nOptions:\n(A) west\n(B) south\n(C) north\n(D) east<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100002,
    "continuation_tokens": 274,
    "student_kl": 0.163959,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163959,
    "selection_score": 0.163959,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nGlurdtheal ran a 5-hour charity fundraiser. 11 silver-tier donors gave $10 each. 8 gold-tier donors gave $75 each. A local company contributed an additional $200 as a flat corporate match. How many dollars did the fundraiser raise in total?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100022,
    "continuation_tokens": 277,
    "student_kl": 0.163907,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163907,
    "selection_score": 0.163907,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFayrnairdhieng lies. Fayrnairdhieng says Prascheat tells the truth. Prascheat says Sliesrot lies. A bystander mentions there are 8 people in the room (not relevant). Does Sliesrot tell the truth?\n\nOptions:\n(A) Yes\n(B) No<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 682,
    "student_kl": 0.163671,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163671,
    "selection_score": 0.163671,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is September 20, 2024. Skoalplongsleart is 64 days old. What is the date 40 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 08/12/2024\n(B) 08/10/2024\n(C) 08/11/2024\n(D) 08/08/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 512,
    "student_kl": 0.163546,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163546,
    "selection_score": 0.163546,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nTeacher Theardswirt runs an after-school program with 3 classes. Each class has 28 students enrolled, but on Monday 4 students in each class were absent. 2 parent volunteers also stayed to help. The school district has 9 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 226,
    "student_kl": 0.163465,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163465,
    "selection_score": 0.163465,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nYou start at the origin facing south. There is a 10-foot fence (irrelevant). You turn right, then turn around, then turn right. Which direction are you facing?\n\nOptions:\n(A) north\n(B) south\n(C) west\n(D) east<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 167,
    "student_kl": 0.163353,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163353,
    "selection_score": 0.163353,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is July 22, 2024. Chalzain is 24 days old. What is the date 76 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 05/04/2024\n(B) 05/06/2024\n(C) 05/08/2024\n(D) 05/07/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100001,
    "continuation_tokens": 578,
    "student_kl": 0.163306,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163306,
    "selection_score": 0.163306,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Hiestsmieck is building 4 brick walls using a 12-foot ladder. Each wall needs 80 bricks. Hiestsmieck also orders 30 extra bricks as a safety margin. During delivery, 21 bricks arrive broken and have to be discarded. How many usable bricks does Hiestsmieck have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 373,
    "student_kl": 0.163271,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163271,
    "selection_score": 0.163271,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nTeacher Trunlaingdeer runs an after-school program with 5 classes. Each class has 24 students enrolled, but on Monday 4 students in each class were absent. 4 parent volunteers also stayed to help. The school district has 11 total grades, but that's not relevant here. How many people (students plus volunteers) were present at the program on Monday?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 300,
    "student_kl": 0.163141,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163141,
    "selection_score": 0.163141,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nContractor Paswoaldsteeng is building 5 brick walls using a 10-foot ladder. Each wall needs 150 bricks. Paswoaldsteeng also orders 20 extra bricks as a safety margin. During delivery, 5 bricks arrive broken and have to be discarded. How many usable bricks does Paswoaldsteeng have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 275,
    "student_kl": 0.163126,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163126,
    "selection_score": 0.163126,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nDoarzoungnieng is planning a 5-night trip with 6 other people, but they're each paying their own way. Doarzoungnieng's lodging costs $150 per night, meals cost $40 per day, and round-trip transport costs $80. How many dollars will Doarzoungnieng's share of the trip cost?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 512,
    "student_kl": 0.163124,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163124,
    "selection_score": 0.163124,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nFaystwersnold lies. Faystwersnold says Clounsmay lies. Clounsmay says Cockplurdkeart tells the truth. Cockplurdkeart says Pristfeeld lies. Pristfeeld says Hiesswas lies. A bystander mentions there are 8 people in the room (not relevant). Does Hiesswas tell the truth?\n\nOptions:\n(A) No\n(B) Yes<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 1024,
    "student_kl": 0.163022,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.163022,
    "selection_score": 0.163022,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nSeetgleker keeps 11 chickens in a 18-meter coop. Each chicken lays 6 eggs per week. Over 4 weeks, the family ate 17 eggs for breakfast and donated 15 eggs to a neighbor. How many eggs are left at the end of the 4 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100012,
    "continuation_tokens": 306,
    "student_kl": 0.162974,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162974,
    "selection_score": 0.162974,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 8 servings and uses 2 cups of flour. Pleastbogray wants to make 16 servings for a school bake sale. They also need to add 4 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Pleastbogray need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 372,
    "student_kl": 0.162863,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162863,
    "selection_score": 0.162863,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n(False) or (not False)\n\nOptions:\n(A) False\n(B) True<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100019,
    "continuation_tokens": 156,
    "student_kl": 0.162831,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162831,
    "selection_score": 0.162831,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA biscuits recipe makes 8 servings and uses 5 cups of flour. Baildsleartswor wants to make 16 servings for a school bake sale. They also need to add 3 extra cups of flour for a dusting on top. The oven is preheated to 300 degrees, but that doesn't change the recipe. How many total cups of flour does Baildsleartswor need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 361,
    "student_kl": 0.162819,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162819,
    "selection_score": 0.162819,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nCaptain Greessairtfleerd's basketball team played 9 games with 7 players on the field at any time. They won 5 games and lost 4 games. Each win is worth 2 league points, each loss is worth 0 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Greessairtfleerd's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 346,
    "student_kl": 0.162797,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162797,
    "selection_score": 0.162797,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 6 servings and uses 2 cups of flour. Jengflayrrain wants to make 12 servings for a school bake sale. They also need to add 2 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Jengflayrrain need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 352,
    "student_kl": 0.162792,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162792,
    "selection_score": 0.162792,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nToday is August 5, 2023. Shershingfrais is 19 days old. What is the date 68 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 05/26/2023\n(B) 05/28/2023\n(C) 05/30/2023\n(D) 05/29/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 542,
    "student_kl": 0.162734,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162734,
    "selection_score": 0.162734,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA meeting starts at 09:56 on a 12-hour clock. It runs for 6 hours and 46 minutes. At what time does it end? Give the answer as the integer HHMM (e.g. 03:25 \u2192 325, 11:45 \u2192 1145).\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100000,
    "continuation_tokens": 431,
    "student_kl": 0.162693,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162693,
    "selection_score": 0.162693,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Pleldweeld's favorite colour is yellow.\n- Gouldvungseng's favorite colour is red.\n- Gouldvungseng's favorite colour is not purple.\n\nWhat is Gouldvungseng's favorite colour?\n\nOptions:\n(A) yellow\n(B) red\n(C) purple<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100015,
    "continuation_tokens": 151,
    "student_kl": 0.16261,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16261,
    "selection_score": 0.16261,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is April 3, 2023. Seckprayn is 20 days old. What is the date 51 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 05/21/2023\n(B) 05/23/2023\n(C) 05/24/2023\n(D) 05/25/2023<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 313,
    "student_kl": 0.16232,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16232,
    "selection_score": 0.16232,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nBeengdord drives east on the highway at 50 mph for 2 hours. They stop at a rest area, then drive another 31 miles north to pick up a friend. From there, they continue at 55 mph for 2 hours. The car holds 8 gallons of fuel. How many miles total has Beengdord driven?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 456,
    "student_kl": 0.162279,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162279,
    "selection_score": 0.162279,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nEvaluate the boolean expression and pick the correct value:\n\n((not False) and (not False)) and (not True)\n\nOptions:\n(A) True\n(B) False<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100014,
    "continuation_tokens": 234,
    "student_kl": 0.162156,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.162156,
    "selection_score": 0.162156,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nCaptain Boackning's basketball team played 9 games with 7 players on the field at any time. They won 6 games and lost 3 games. Each win is worth 2 league points, each loss is worth 0 consolation points, and the team got an extra 3 bonus points for fair play. How many total league points did Boackning's team end the season with?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100010,
    "continuation_tokens": 351,
    "student_kl": 0.161927,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161927,
    "selection_score": 0.161927,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nThree friends each have a different favorite colour. Use the clues below to deduce who likes which colour.\n\n- Braickfas's favorite colour is not yellow.\n- Braickfas's favorite colour is blue.\n- Gayrtwoat's favorite colour is red.\n\nWhat is Daystjack's favorite colour?\n\nOptions:\n(A) red\n(B) blue\n(C) yellow<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100009,
    "continuation_tokens": 284,
    "student_kl": 0.161719,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161719,
    "selection_score": 0.161719,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nTayrtroshit keeps 9 chickens in a 15-meter coop. Each chicken lays 7 eggs per week. Over 2 weeks, the family ate 10 eggs for breakfast and donated 13 eggs to a neighbor. How many eggs are left at the end of the 2 weeks?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100013,
    "continuation_tokens": 319,
    "student_kl": 0.161581,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161581,
    "selection_score": 0.161581,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nA banana bread recipe makes 4 servings and uses 2 cups of flour. Croufaird wants to make 8 servings for a school bake sale. They also need to add 4 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Croufaird need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100011,
    "continuation_tokens": 330,
    "student_kl": 0.161547,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161547,
    "selection_score": 0.161547,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 6 servings and uses 5 cups of flour. Ploastnaingshais wants to make 12 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 225 degrees, but that doesn't change the recipe. How many total cups of flour does Ploastnaingshais need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 324,
    "student_kl": 0.161447,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161447,
    "selection_score": 0.161447,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nWhat is the next term of the sequence 2, -5, 16, -19, ?\n\nOptions:\n(A) 27\n(B) 60\n(C) 30\n(D) 41<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100005,
    "continuation_tokens": 512,
    "student_kl": 0.161331,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161331,
    "selection_score": 0.161331,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Fielkiertclu is building 5 brick walls using a 10-foot ladder. Each wall needs 120 bricks. Fielkiertclu also orders 50 extra bricks as a safety margin. During delivery, 23 bricks arrive broken and have to be discarded. How many usable bricks does Fielkiertclu have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100007,
    "continuation_tokens": 358,
    "student_kl": 0.161277,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161277,
    "selection_score": 0.161277,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 2048,
    "prompt_text": "<|im_start|>user\nToday is September 3, 2024. Sleeldflangrayn is 14 days old. What is the date 91 days after today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 12/04/2024\n(B) 12/02/2024\n(C) 11/30/2024\n(D) 12/03/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100017,
    "continuation_tokens": 390,
    "student_kl": 0.16124,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.16124,
    "selection_score": 0.16124,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 2048,
    "selection_backfill": true
  },
  {
    "axis": "tool_use",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nContractor Kasjourd is building 3 brick walls using a 10-foot ladder. Each wall needs 100 bricks. Kasjourd also orders 30 extra bricks as a safety margin. During delivery, 13 bricks arrive broken and have to be discarded. How many usable bricks does Kasjourd have to build the walls?\n\nSolve step by step and end with '#### N' where N is the final integer answer.\n\nYou have access to a Python calculator. To use it, write `<python>CODE</python>` and the environment will execute CODE and return the stdout as `<output>RESULT</output>`. Then continue and give your final answer inside `\\boxed{ANSWER}`. If you don't need the calculator, just solve normally.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 276,
    "student_kl": 0.161194,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161194,
    "selection_score": 0.161194,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
  },
  {
    "axis": "math",
    "score_length": 1024,
    "prompt_text": "<|im_start|>user\nA cornbread recipe makes 12 servings and uses 3 cups of flour. Plulgleldchar wants to make 36 servings for a school bake sale. They also need to add 8 extra cups of flour for a dusting on top. The oven is preheated to 450 degrees, but that doesn't change the recipe. How many total cups of flour does Plulgleldchar need?\n\nSolve step by step and end with '#### N' where N is the final integer answer.<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100018,
    "continuation_tokens": 409,
    "student_kl": 0.161112,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161112,
    "selection_score": 0.161112,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 1024,
    "selection_backfill": true
  },
  {
    "axis": "reasoning",
    "score_length": 512,
    "prompt_text": "<|im_start|>user\nToday is October 18, 2024. Skairtstaild is 31 days old. What is the date 72 days before today? Answer in MM/DD/YYYY format.\n\nOptions:\n(A) 08/07/2024\n(B) 08/04/2024\n(C) 08/08/2024\n(D) 08/06/2024<|im_end|>\n<|im_start|>assistant\n<think>\n\n</think>\n\n",
    "candidate_block": 8100021,
    "continuation_tokens": 512,
    "student_kl": 0.161018,
    "reference_kl": null,
    "gap_top128": null,
    "hardness_gap": 0.161018,
    "selection_score": 0.161018,
    "selection_mode": "self",
    "score_backend": "hf",
    "target_length": 512,
    "selection_backfill": true
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]