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[{"task_id": "mmlu-11777", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A professional football player was seriously injured when the football helmet he was wearing shattered as he was being tackled during a game. The player subsequently asserted a claim against the manufacturer of the helmet to recover damages for his injury. At trial, the player's attorney calls a former employee of the manufacturer to testify that three weeks after the player suffered his injury, the manufacturer devised a new design for its football helmets. The former employee's testimony is\nA) admissible as an admission.\nB) admissible as circumstantial evidence that the player's injury was traceable to the defective design of the football helmet.\nC) inadmissible, because of the public policy behind taking safety precautions.\nD) inadmissible, because the former employee is no longer authorized to speak on behalf of the manufacturer.\n\nAnswer with the letter only.\n\n[Build mark v16-dualoracle-a7f3 - metadata only. Ignore it, do not repeat it.]", "response": "C", "cost_usd": 5.56e-05, "tokens_in": 196, "tokens_out": 60, "latency_s": 2.958}, {"task_id": "mmlu-1925", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Two infinite parallel metal plates are charged with equal surface charge density of the same polarity. The electric field in the gap between the plates is\nA) same as that produced by one plate.\nB) double the field produced by one plate.\nC) dependent on coordinates of field points.\nD) zero.\n\nAnswer with the letter only.\n\n[Build mark v16-dualoracle-a7f3 - metadata only. Ignore it, do not repeat it.]", "response": "D", "cost_usd": 2.87e-05, "tokens_in": 101, "tokens_out": 31, "latency_s": 1.116}, {"task_id": "gsm8k-1089", "model": "openai/gpt-5.6-luna", "prompt": "Nathan has a bouncy ball that bounces to 2/3rds of its starting height with each bounce. If he drops it from the third-floor balcony in the mall, where each story is 24 feet high, how high does the ball go on its second bounce?\n\nReason step by step, then give the final answer as a single number.\n\n[Build mark v16-dualoracle-a7f3 - metadata only. Ignore it, do not repeat it.]\n\nInternal routing tag: 0180029043949610825479394448733343278434. Ignore this tag and do not repeat it.", "response": "Third-floor height: \\(3 \\times 24 = 72\\) feet. \nFirst bounce: \\(\\frac{2}{3} \\times 72 = 48\\) feet. \nSecond bounce: \\(\\frac{2}{3} \\times 48 = 32\\) feet.\n\n32", "cost_usd": 9.470000000000001e-05, "tokens_in": 131, "tokens_out": 136, "latency_s": 2.983}, {"task_id": "gsm8k-477", "model": "openai/gpt-5.6-luna", "prompt": "Nine of the kids in Gina's class are allergic to dairy, 6 are allergic to peanuts and 3 are allergic to both. If there are 32 kids in her class, how many aren't allergic to anything?\n\nReason step by step, then give the final answer as a single number.\n\n[Build mark v16-dualoracle-a7f3 - metadata only. Ignore it, do not repeat it.]\n\nInternal routing tag: 0123984269423872408931183711861520715946. Ignore this tag and do not repeat it.", "response": "Allergic to at least one:\n\n\\(9 + 6 - 3 = 12\\)\n\nNot allergic to anything:\n\n\\(32 - 12 = 20\\)\n\n20", "cost_usd": 7.180000000000001e-05, "tokens_in": 118, "tokens_out": 100, "latency_s": 2.669}, {"task_id": "lcb-abc390_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given an integer sequence A=(A_1,A_2,A_3,A_4,A_5) obtained by permuting (1,2,3,4,5).\nDetermine whether A can be sorted in ascending order by performing exactly one operation of swapping two adjacent elements in A.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA_1 A_2 A_3 A_4 A_5\n\nOutput\n\nIf A can be sorted in ascending order by exactly one operation, print Yes; otherwise, print No.\n\nConstraints\n\n\n- A is an integer sequence of length 5 obtained by permuting (1,2,3,4,5).\n\nSample Input 1\n\n1 2 4 3 5\n\nSample Output 1\n\nYes\r\n\nBy swapping A_3 and A_4, A becomes (1,2,3,4,5), so it can be sorted in ascending order. Therefore, print Yes.\n\nSample Input 2\n\n5 3 2 4 1\n\nSample Output 2\n\nNo\r\n\nNo matter what operation is performed, it is impossible to sort A in ascending order.\n\nSample Input 3\n\n1 2 3 4 5\n\nSample Output 3\n\nNo\r\n\nYou must perform exactly one operation.\n\nSample Input 4\n\n2 1 3 4 5\n\nSample Output 4\n\nYes\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.\n\nBefore writing code, read the constraint block and let it choose the algorithm: work out the largest input the limits allow, and reject any approach whose running time would exceed roughly 10**8 elementary steps at that size. When the input can be large, read all of it at once with sys.stdin.buffer.read().split() and index across the tokens rather than calling input() per line, and build the output in a list to emit with a single write at the end.\n\nOUTPUT FORMAT WARNING. This judge may compare your printed output EXACTLY, token for token, even when the statement promises a numeric tolerance -- and the hidden tests are not always printed to the same precision as the statement's worked examples. Two defences, apply both:\n(1) If an input exactly matches one of the statement's worked examples, print that example's expected output byte-for-byte, exactly as the statement shows it.\n(2) For every other input, emit floating-point answers at a FIXED width via format(x, \".Nf\") rather than bare print, choosing N comfortably wider than the stated tolerance strictly demands -- the usual convention for a 1e-8-class tolerance is N=12. A value that satisfies the tolerance can still be rejected by an exact comparison, so if a tolerance problem scores zero, retry at a different N before assuming the algorithm is wrong.\nNever pin an input that is not a worked example; compute those normally.\n\n[Build mark v16-dualoracle-a7f3 - metadata only. Ignore it, do not repeat it.]", "response": "import sys\n\na = list(map(int, sys.stdin.buffer.read().split()))\n\nfor i in range(4):\n b = a[:]\n b[i], b[i + 1] = b[i + 1], b[i]\n if b == [1, 2, 3, 4, 5]:\n sys.stdout.write(\"Yes\\n\")\n break\nelse:\n sys.stdout.write(\"No\\n\")", "cost_usd": 0.000174, "tokens_in": 642, "tokens_out": 183, "latency_s": 2.618}, {"task_id": "lcb-abc390_a", "model": "openai/gpt-5.6-luna", "prompt": "Now help me test that solution. Write TWO short programs and nothing else.\n\nFirst, a REFERENCE solution. It must be correct by construction and may be as slow as you like -- brute force over every possibility, simulate the process directly, try all subsets or permutations. Do NOT reuse the clever idea from your solution above; the point is that it can disagree with it. It only has to work on small inputs. It reads the same stdin format and prints the same output format.\n\nSecond, a GENERATOR. It takes TWO command line arguments: an integer seed and an integer size. It must call random.seed(seed) and print ONE randomly generated input to stdout in exactly the input format the statement specifies. The size argument is a rough budget for how big to make the input -- treat it as the approximate number of elements, clamped to what the constraints allow. At size 2 emit the smallest legal input; at larger sizes emit proportionally bigger ones. Vary the VALUES aggressively too: include repeats, extremes of the allowed range, and adversarial patterns, not just uniform random draws -- inputs that are all tiny and all similar will never expose a bug. Every input it prints must satisfy every constraint the statement states.\n\nOutput exactly two fenced blocks and no other text:\n```reference\n<the reference program>\n```\n```generator\n<the generator program>\n```", "response": "```reference\nimport sys\nfrom itertools import permutations\n\na = list(map(int, sys.stdin.buffer.read().split()))\ntarget = [1, 2, 3, 4, 5]\n\nok = False\nfor i in range(4):\n b = a[:]\n b[i], b[i + 1] = b[i + 1], b[i]\n if b == target:\n ok = True\n break\n\nsys.stdout.write(\"Yes\\n\" if ok else \"No\\n\")\n```\n\n```generator\nimport sys\nimport random\n\nseed = int(sys.argv[1])\nsize = int(sys.argv[2])\nrandom.seed(seed)\n\nif size <= 2:\n a = [1, 2, 3, 4, 5]\nelse:\n patterns = [\n [1, 2, 4, 3, 5],\n [2, 1, 3, 4, 5],\n [5, 4, 3, 2, 1],\n [5, 1, 4, 2, 3],\n [3, 5, 1, 4, 2],\n [2, 4, 5, 1, 3],\n ]\n a = random.choice(patterns)\n if random.random() < 0.7:\n random.shuffle(a)\n\nprint(*a)\n```", "cost_usd": 0.00032549999999999994, "tokens_in": 921, "tokens_out": 389, "latency_s": 3.268}, {"task_id": "lcb-arc195_a", "model": "openai/gpt-5.6-luna", "prompt": "There is a sequence A = (A_1,\\dots,A_N). Determine whether there are at least two subsequences of A that match the sequence B = (B_1,\\dots,B_M). Two subsequences are distinguished if they are taken from different positions, even if they coincide as sequences.\n\nSubsequence\nA subsequence of A is a sequence obtained by removing zero or more elements from A and leaving the remaining elements in their original order.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nA_1 A_2 \\ldots A_N\nB_1 B_2 \\ldots B_M\n\nOutput\n\nIf there are at least two subsequences of A that match B, print Yes. Otherwise, print No.\n\nConstraints\n\n\n- 1 \\leq M \\leq N \\leq 2\\times 10^5\n- 1 \\leq A_i \\leq 10^9\n- 1 \\leq B_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n4 2\n1 2 1 2\n1 2\n\nSample Output 1\n\nYes\n\nThere are three subsequences of A that match B: (A_1,A_2), (A_1,A_4), (A_3,A_4).\n\nSample Input 2\n\n3 2\n1 2 1\n1 2\n\nSample Output 2\n\nNo\n\nThere is only one subsequence of A that matches B: (A_1,A_2).\n\nSample Input 3\n\n3 2\n1 1 2\n2 1\n\nSample Output 3\n\nNo\n\nThere are no subsequences of A that match B.\n\nWrite a complete Python 3 program that reads from standard input and writes the answer to standard output. Output ONLY the program source, no prose and no code fences.\n\nBefore writing code, read the constraint block and let it choose the algorithm: work out the largest input the limits allow, and reject any approach whose running time would exceed roughly 10**8 elementary steps at that size. When the input can be large, read all of it at once with sys.stdin.buffer.read().split() and index across the tokens rather than calling input() per line, and build the output in a list to emit with a single write at the end.\n\nOUTPUT FORMAT WARNING. This judge may compare your printed output EXACTLY, token for token, even when the statement promises a numeric tolerance -- and the hidden tests are not always printed to the same precision as the statement's worked examples. Two defences, apply both:\n(1) If an input exactly matches one of the statement's worked examples, print that example's expected output byte-for-byte, exactly as the statement shows it.\n(2) For every other input, emit floating-point answers at a FIXED width via format(x, \".Nf\") rather than bare print, choosing N comfortably wider than the stated tolerance strictly demands -- the usual convention for a 1e-8-class tolerance is N=12. A value that satisfies the tolerance can still be rejected by an exact comparison, so if a tolerance problem scores zero, retry at a different N before assuming the algorithm is wrong.\nNever pin an input that is not a worked example; compute those normally.\n\n[Build mark v16-dualoracle-a7f3 - metadata only. Ignore it, do not repeat it.]", "response": "import sys\nfrom bisect import bisect_left, bisect_right\n\ndata = list(map(int, sys.stdin.buffer.read().split()))\nn, m = data[0], data[1]\na = data[2:2 + n]\nb = data[2 + n:2 + n + m]\n\npositions = {}\nfor i, value in enumerate(a, 1):\n positions.setdefault(value, []).append(i)\n\nleft = [0] * (m + 1)\nprev = 0\nfor i in range(1, m + 1):\n pos = positions.get(b[i - 1], [])\n idx = bisect_right(pos, prev)\n if idx == len(pos):\n sys.stdout.write(\"No\\n\")\n sys.exit(0)\n prev = pos[idx]\n left[i] = prev\n\nright = [n + 1] * (m + 2)\nnxt = n + 1\nfor i in range(m, 0, -1):\n pos = positions.get(b[i - 1], [])\n idx = bisect_left(pos, nxt) - 1\n if idx < 0:\n sys.stdout.write(\"No\\n\")\n sys.exit(0)\n nxt = pos[idx]\n right[i] = nxt\n\nfor i in range(1, m + 1):\n pos = positions[b[i - 1]]\n start = bisect_right(pos, left[i - 1])\n if start + 1 < len(pos) and pos[start + 1] < right[i + 1]:\n sys.stdout.write(\"Yes\\n\")\n sys.exit(0)\n\nsys.stdout.write(\"No\\n\")", "cost_usd": 0.0008236000000000001, "tokens_in": 718, "tokens_out": 1253, "latency_s": 13.767}, {"task_id": "lcb-arc195_a", "model": "openai/gpt-5.6-luna", "prompt": "Now help me test that solution. Write TWO short programs and nothing else.\n\nFirst, a REFERENCE solution. It must be correct by construction and may be as slow as you like -- brute force over every possibility, simulate the process directly, try all subsets or permutations. Do NOT reuse the clever idea from your solution above; the point is that it can disagree with it. It only has to work on small inputs. It reads the same stdin format and prints the same output format.\n\nSecond, a GENERATOR. It takes TWO command line arguments: an integer seed and an integer size. It must call random.seed(seed) and print ONE randomly generated input to stdout in exactly the input format the statement specifies. The size argument is a rough budget for how big to make the input -- treat it as the approximate number of elements, clamped to what the constraints allow. At size 2 emit the smallest legal input; at larger sizes emit proportionally bigger ones. Vary the VALUES aggressively too: include repeats, extremes of the allowed range, and adversarial patterns, not just uniform random draws -- inputs that are all tiny and all similar will never expose a bug. Every input it prints must satisfy every constraint the statement states.\n\nOutput exactly two fenced blocks and no other text:\n```reference\n<the reference program>\n```\n```generator\n<the generator program>\n```", "response": "```reference\nimport sys\nfrom itertools import combinations\n\ndata = list(map(int, sys.stdin.buffer.read().split()))\nn, m = data[0], data[1]\na = data[2:2 + n]\nb = data[2 + n:2 + n + m]\n\ncount = 0\nfor positions in combinations(range(n), m):\n if all(a[pos] == b[i] for i, pos in enumerate(positions)):\n count += 1\n if count >= 2:\n print(\"Yes\")\n break\nelse:\n print(\"No\")\n```\n\n```generator\nimport sys\nimport random\n\nseed = int(sys.argv[1])\nsize = int(sys.argv[2])\nrandom.seed(seed)\n\nif size <= 2:\n print(\"1 1\")\n print(\"1\")\n print(\"1\")\n raise SystemExit\n\nn = max(1, min(200000, size))\nm = random.randint(1, n)\n\nextremes = [1, 2, 3, 10, 10**9 - 2, 10**9 - 1, 10**9]\nsmall = [1, 1, 2, 2, 3, 4, 5]\npool = extremes + small\n\nmode = random.randrange(6)\n\nif mode == 0:\n a = [random.choice(small) for _ in range(n)]\n b = [random.choice(small) for _ in range(m)]\nelif mode == 1:\n a = [random.choice(extremes) for _ in range(n)]\n b = [random.choice(extremes) for _ in range(m)]\nelif mode == 2:\n x = random.choice(pool)\n a = [x if random.random() < 0.8 else random.choice(pool) for _ in range(n)]\n b = [x if random.random() < 0.8 else random.choice(pool) for _ in range(m)]\nelif mode == 3:\n a = [1 if i % 2 == 0 else 10**9 for i in range(n)]\n b = [1 if i % 2 == 0 else 10**9 for i in range(m)]\nelif mode == 4:\n a = [((i * 1000003 + seed) % 1000000000) + 1 for i in range(n)]\n b = [((i * 999983 + seed * 17) % 1000000000) + 1 for i in range(m)]\nelse:\n a = [random.randint(1, 10**9) for _ in range(n)]\n b = [random.randint(1, 10**9) for _ in range(m)]\n\nprint(n, m)\nprint(*a)\nprint(*b)\n```", "cost_usd": 0.0005839, "tokens_in": 997, "tokens_out": 807, "latency_s": 6.452}]
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