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+[{"task_id": "mmlu-11334", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A new gang member, hoping to impress the gang's leader, pointed a gun at a pedestrian and ordered her to give him her expensive watch, which she did. The gang member then tossed the watch to the gang leader, who was standing nearby. Although totally surprised by this act, the gang leader put the watch in his pocket. The pedestrian ran away. What crime did the gang leader commit?\nA) Accessory after the fact to robbery.\nB) Accomplice to robbery.\nC) Conspiracy to commit robbery.\nD) Receiving stolen property.\n\nAnswer with the letter only.", "response": "D", "cost_usd": 0.0001118, "tokens_in": 128, "tokens_out": 165, "latency_s": 3.949}, {"task_id": "mmlu-9646", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Which of the following rules regarding the interconversion of fuels are central to the integration of metabolic pathways?\n\nA) Fatty acids can be made from and converted to carbohydrates and amino acids\nB) Carbohydrates can be made from and converted to amino acids and fatty acids\nC) Fatty acids can be made from but not converted to carbohydrates and amino acids\nD) Amino acids can be made from and converted to fatty acids\n\nAnswer with the letter only.", "response": "B", "cost_usd": 1.3400000000000014e-05, "tokens_in": 104, "tokens_out": 5, "latency_s": 0.771}, {"task_id": "gsm8k-707", "model": "openai/gpt-5.6-luna", "prompt": "Colorado City uses 40% of the water from the Colorado River. If 80% of that water is used for industrial purposes, what percent of the river's total water is used by the city for non-industrial purposes?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and privately verify arithmetic, signs, rounding, and boundary assumptions. Put only the final numeric result on the last line.", "response": "Colorado City uses 40% of the river\u2019s total water.\n\nNon-industrial use is the remaining 20% of the city\u2019s water:\n\n\\(40\\% \\times 20\\% = 8\\%\\)\n\n8%", "cost_usd": 7.38e-05, "tokens_in": 96, "tokens_out": 107, "latency_s": 2.492}, {"task_id": "gsm8k-780", "model": "openai/gpt-5.6-luna", "prompt": "Ava and Emma want to know who is better at the new video game Ava got for her birthday. They are each going to play one level and whoever has the highest score wins. They receive 10 points for every enemy they jump on, 5 points for each berry they collect, and 30 points for every second left on the timer when they finish the level. If Ava jumps on 8 more enemies than Emma and collects 3 more berries, but finishes the level 4 seconds slower, what is the difference between their two scores?\n\nReason step by step, then give the final answer as a single number.\n\nSolve in the requested units and privately verify arithmetic, signs, rounding, and boundary assumptions. Put only the final numeric result on the last line.", "response": "Ava earns:\n\n- \\(8 \\times 10 = 80\\) more points from enemies.\n- \\(3 \\times 5 = 15\\) more points from berries.\n- Finishing 4 seconds slower means \\(4 \\times 30 = 120\\) fewer points.\n\nNet difference:\n\n\\[\n80+15-120=-25\n\\]\n\nSo Ava\u2019s score is 25 points lower, meaning the difference between their scores is:\n\n25", "cost_usd": 0.0001222, "tokens_in": 160, "tokens_out": 177, "latency_s": 2.826}, {"task_id": "lcb-abc400_b", "model": "openai/gpt-5.6-luna", "prompt": "You are given two positive integers N and M.\nLet X = \\displaystyle\\sum_{i = 0}^{M} N^i. If X \\leq 10^9, print the value of X. If X > 10^9, print inf.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\n\nOutput\n\nPrint the value of X or inf as specified by the problem statement.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^9\n- 1 \\leq M \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n7 3\n\nSample Output 1\n\n400\r\n\nX = 1 + 7 + 49 + 343 = 400. Since 400 \\leq 10^9, print 400.\n\nSample Input 2\n\n1000000 2\n\nSample Output 2\n\ninf\r\n\nX = 1000001000001 > 10^9, so print inf.\n\nSample Input 3\n\n999999999 1\n\nSample Output 3\n\n1000000000\n\nSample Input 4\n\n998244353 99\n\nSample Output 4\n\ninf\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\nDerive the algorithm from the complete specification and maximum constraints. Privately construct a small direct specification and try to falsify the proposed algorithm. Check ordering, multiplicity, repeated values, boundaries, state changes, and complexity. Trace every published example. The execution harness compares output tokens exactly even when the problem prose grants mathematical tolerance. Match the required canonical representation, precision, rounding, ordering, and separators shown by the statement and examples. Do not print extra precision merely because it is available. Return only one complete raw Python 3 program without Markdown, fences, or explanation.", "response": "n, m = map(int, input().split())\n\nlimit = 10**9\ntotal = 0\npower = 1\n\nfor _ in range(m + 1):\n    total += power\n    if total > limit:\n        print(\"inf\")\n        break\n    power *= n\nelse:\n    print(total)\n", "cost_usd": 8.290000000000001e-05, "tokens_in": 403, "tokens_out": 71, "latency_s": 1.263}, {"task_id": "lcb-abc400_b", "model": "openai/gpt-5.6-luna", "prompt": "You are given two positive integers N and M.\nLet X = \\displaystyle\\sum_{i = 0}^{M} N^i. If X \\leq 10^9, print the value of X. If X > 10^9, print inf.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\n\nOutput\n\nPrint the value of X or inf as specified by the problem statement.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^9\n- 1 \\leq M \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n7 3\n\nSample Output 1\n\n400\r\n\nX = 1 + 7 + 49 + 343 = 400. Since 400 \\leq 10^9, print 400.\n\nSample Input 2\n\n1000000 2\n\nSample Output 2\n\ninf\r\n\nX = 1000001000001 > 10^9, so print inf.\n\nSample Input 3\n\n999999999 1\n\nSample Output 3\n\n1000000000\n\nSample Input 4\n\n998244353 99\n\nSample Output 4\n\ninf\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\nWork independently from the statement and do not assume any candidate implementation. Write a correctness-first oracle for small legal inputs using direct simulation or exhaustive search. Also write a generator accepting seed and size arguments, seeding Python random, and printing one varied legal input. Systematically include legal ties and equalities, repeated values, minimum counts, endpoints, mandatory final transitions, and choices where an equal local action changes a later opportunity. Vary these boundary families from the seed instead of emitting a fixed example. The oracle must not reuse the efficient algorithm requested by the statement. The execution harness compares output tokens exactly even when the prose permits numerical tolerance. Reproduce every published output token exactly and infer one canonical representation for unseen outputs from the statement and examples without inventing extra precision. Return exactly two fenced blocks named oracle and generator, with no other text.", "response": "```oracle\nimport sys\n\ndef main():\n    n, m = map(int, sys.stdin.readline().split())\n    total = 0\n    power = 1\n\n    for _ in range(m + 1):\n        total += power\n        if total > 10**9:\n            print(\"inf\")\n            return\n        power *= n\n\n    print(total)\n\nif __name__ == \"__main__\":\n    main()\n```\n\n```generator\nimport random\nimport sys\n\ndef main():\n    seed = int(sys.argv[1])\n    size = max(1, int(sys.argv[2]))\n    random.seed(seed)\n\n    family = random.randrange(10)\n\n    if family == 0:\n        n = 1\n        m = random.randint(1, min(100, size))\n    elif family == 1:\n        n = 10**9\n        m = 1\n    elif family == 2:\n        n = 999999999\n        m = 1\n    elif family == 3:\n        n = random.randint(1, 10)\n        m = random.randint(1, 100)\n    elif family == 4:\n        m = random.randint(1, min(100, max(1, size)))\n        n = random.randint(10**8, 10**9)\n    elif family == 5:\n        m = 2\n        n = random.choice([31622, 31623, 999999, 1000000])\n    elif family == 6:\n        n = random.choice([2, 3, 7, 998244353])\n        m = random.choice([1, 2, 3, 99, 100])\n    elif family == 7:\n        n = random.randint(1, min(10**9, max(1, size)))\n        m = 100\n    elif family == 8:\n        n = random.choice([999999998, 999999999, 10**9])\n        m = random.choice([1, 2])\n    else:\n        n = random.randint(1, 10**9)\n        m = random.randint(1, 100)\n\n    print(n, m)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0005664, "tokens_in": 456, "tokens_out": 868, "latency_s": 9.294}, {"task_id": "lcb-abc400_d", "model": "openai/gpt-5.6-luna", "prompt": "Takahashi is about to go buy eel at a fish shop.\nThe town where he lives is divided into a grid of H rows and W columns. Each cell is either a road or a wall.\r\nLet us denote the cell at the i-th row from the top (1\\leq i \\leq H) and the j-th column from the left (1\\leq j \\leq W) as cell (i,j).\r\nInformation about each cell is given by H strings S_1,S_2,\\ldots,S_H, each of length W. Specifically, if the j-th character of S_i (1\\leq i \\leq H,1\\leq j\\leq W) is ., cell (i,j) is a road; if it is #, cell (i,j) is a wall.\nHe can repeatedly perform the following two types of actions in any order:\n\n- Move to an adjacent cell (up, down, left, or right) that is within the town and is a road.\n- Choose one of the four directions (up, down, left, or right) and perform a front kick in that direction.\r\n  When he performs a front kick, for each of the cells at most 2 steps away in that direction from the cell he is currently in, if that cell is a wall, it becomes a road.\r\n  If some of the cells at most 2 steps away are outside the town, a front kick can still be performed, but anything outside the town does not change.\n\nHe starts in cell (A,B), and he wants to move to the fish shop in cell (C,D).\r\nIt is guaranteed that both the cell where he starts and the cell with the fish shop are roads.\r\nFind the minimum number of front kicks he needs in order to reach the fish shop.\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W\r\nS_1\r\nS_2\r\n\\vdots\r\nS_H\r\nA B C D\n\nOutput\n\nPrint the minimum number of front kicks needed for Takahashi to reach the fish shop.\n\nConstraints\n\n\n- 1\\leq H\\leq 1000\n- 1\\leq W\\leq 1000\n- Each S_i is a string of length W consisting of . and #.\n- 1\\leq A,C\\leq H\n- 1\\leq B,D\\leq W\n- (A,B)\\neq (C,D)\n- H, W, A, B, C, and D are integers.\n- The cell where Takahashi starts and the cell with the fish shop are roads.\n\nSample Input 1\n\n10 10\r\n..........\r\n#########.\r\n#.......#.\r\n#..####.#.\r\n##....#.#.\r\n#####.#.#.\r\n.##.#.#.#.\r\n###.#.#.#.\r\n###.#.#.#.\r\n#.....#...\r\n1 1 7 1\n\nSample Output 1\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nBy repeatedly moving to adjacent road cells, he can reach cell (7,4).\r\nIf he performs a front kick to the left from cell (7,4), cells (7,3) and (7,2) turn from walls to roads.\r\nThen, by continuing to move through road cells (including those that have become roads), he can reach the fish shop in cell (7,1).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 2\n\n2 2\r\n.#\r\n#.\r\n1 1 2 2\n\nSample Output 2\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nWhen he performs a front kick to the right, cell (1,2) turns from a wall to a road.\r\nThe cell two steps to the right of (1,1) is outside the town, so it does not change.\r\nThen, he can move to cell (1,2) and then to the fish shop in cell (2,2).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 3\n\n1 3\r\n.#.\r\n1 1 1 3\n\nSample Output 3\n\n1\r\n\nWhen performing a front kick, it is fine if the fish shop\u2019s cell is within the cells that could be turned into a road. Specifically, the fish shop\u2019s cell is a road from the beginning, so it remains unchanged; particularly, the shop is not destroyed by the front kick.\n\nSample Input 4\n\n20 20\r\n####################\r\n##...##....###...###\r\n#.....#.....#.....##\r\n#..#..#..#..#..#..##\r\n#..#..#....##..#####\r\n#.....#.....#..#####\r\n#.....#..#..#..#..##\r\n#..#..#.....#.....##\r\n#..#..#....###...###\r\n####################\r\n####################\r\n##..#..##...###...##\r\n##..#..#.....#.....#\r\n##..#..#..#..#..#..#\r\n##..#..#..#..#..#..#\r\n##.....#..#..#..#..#\r\n###....#..#..#..#..#\r\n#####..#.....#.....#\r\n#####..##...###...##\r\n####################\r\n3 3 18 18\n\nSample Output 4\n\n3\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\nDerive the algorithm from the complete specification and maximum constraints. Privately construct a small direct specification and try to falsify the proposed algorithm. Check ordering, multiplicity, repeated values, boundaries, state changes, and complexity. Trace every published example. The execution harness compares output tokens exactly even when the problem prose grants mathematical tolerance. Match the required canonical representation, precision, rounding, ordering, and separators shown by the statement and examples. Do not print extra precision merely because it is available. Return only one complete raw Python 3 program without Markdown, fences, or explanation.", "response": "import sys\nfrom collections import deque\nfrom array import array\n\ndef main():\n    input = sys.stdin.readline\n    H, W = map(int, input().split())\n    grid = [input().strip() for _ in range(H)]\n    A, B, C, D = map(int, input().split())\n    A -= 1\n    B -= 1\n    C -= 1\n    D -= 1\n\n    n = H * W\n    start = A * W + B\n    goal = C * W + D\n\n    dist = array('i', [-1]) * n\n    dist[start] = 0\n    dq = deque([start])\n\n    directions = ((1, 0), (-1, 0), (0, 1), (0, -1))\n\n    while dq:\n        v = dq.popleft()\n        if v == goal:\n            break\n\n        r, c = divmod(v, W)\n        nd = dist[v]\n\n        for dr, dc in directions:\n            nr = r + dr\n            nc = c + dc\n            if 0 <= nr < H and 0 <= nc < W:\n                u = nr * W + nc\n                if grid[nr][nc] == '.' and dist[u] == -1:\n                    dist[u] = nd\n                    dq.appendleft(u)\n\n        kick_dist = nd + 1\n        for dr, dc in directions:\n            for step in (1, 2):\n                nr = r + dr * step\n                nc = c + dc * step\n                if 0 <= nr < H and 0 <= nc < W:\n                    u = nr * W + nc\n                    if dist[u] == -1 or dist[u] > kick_dist:\n                        dist[u] = kick_dist\n                        dq.append(u)\n\n    print(dist[goal])\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.000718375, "tokens_in": 1322, "tokens_out": 922, "latency_s": 9.35}, {"task_id": "lcb-abc400_d", "model": "openai/gpt-5.6-luna", "prompt": "Takahashi is about to go buy eel at a fish shop.\nThe town where he lives is divided into a grid of H rows and W columns. Each cell is either a road or a wall.\r\nLet us denote the cell at the i-th row from the top (1\\leq i \\leq H) and the j-th column from the left (1\\leq j \\leq W) as cell (i,j).\r\nInformation about each cell is given by H strings S_1,S_2,\\ldots,S_H, each of length W. Specifically, if the j-th character of S_i (1\\leq i \\leq H,1\\leq j\\leq W) is ., cell (i,j) is a road; if it is #, cell (i,j) is a wall.\nHe can repeatedly perform the following two types of actions in any order:\n\n- Move to an adjacent cell (up, down, left, or right) that is within the town and is a road.\n- Choose one of the four directions (up, down, left, or right) and perform a front kick in that direction.\r\n  When he performs a front kick, for each of the cells at most 2 steps away in that direction from the cell he is currently in, if that cell is a wall, it becomes a road.\r\n  If some of the cells at most 2 steps away are outside the town, a front kick can still be performed, but anything outside the town does not change.\n\nHe starts in cell (A,B), and he wants to move to the fish shop in cell (C,D).\r\nIt is guaranteed that both the cell where he starts and the cell with the fish shop are roads.\r\nFind the minimum number of front kicks he needs in order to reach the fish shop.\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W\r\nS_1\r\nS_2\r\n\\vdots\r\nS_H\r\nA B C D\n\nOutput\n\nPrint the minimum number of front kicks needed for Takahashi to reach the fish shop.\n\nConstraints\n\n\n- 1\\leq H\\leq 1000\n- 1\\leq W\\leq 1000\n- Each S_i is a string of length W consisting of . and #.\n- 1\\leq A,C\\leq H\n- 1\\leq B,D\\leq W\n- (A,B)\\neq (C,D)\n- H, W, A, B, C, and D are integers.\n- The cell where Takahashi starts and the cell with the fish shop are roads.\n\nSample Input 1\n\n10 10\r\n..........\r\n#########.\r\n#.......#.\r\n#..####.#.\r\n##....#.#.\r\n#####.#.#.\r\n.##.#.#.#.\r\n###.#.#.#.\r\n###.#.#.#.\r\n#.....#...\r\n1 1 7 1\n\nSample Output 1\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nBy repeatedly moving to adjacent road cells, he can reach cell (7,4).\r\nIf he performs a front kick to the left from cell (7,4), cells (7,3) and (7,2) turn from walls to roads.\r\nThen, by continuing to move through road cells (including those that have become roads), he can reach the fish shop in cell (7,1).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 2\n\n2 2\r\n.#\r\n#.\r\n1 1 2 2\n\nSample Output 2\n\n1\r\n\nTakahashi starts in cell (1,1).\r\nWhen he performs a front kick to the right, cell (1,2) turns from a wall to a road.\r\nThe cell two steps to the right of (1,1) is outside the town, so it does not change.\r\nThen, he can move to cell (1,2) and then to the fish shop in cell (2,2).\nIn this case, the number of front kicks performed is 1, and it is impossible to reach the fish shop without performing any front kicks, so print 1.\n\nSample Input 3\n\n1 3\r\n.#.\r\n1 1 1 3\n\nSample Output 3\n\n1\r\n\nWhen performing a front kick, it is fine if the fish shop\u2019s cell is within the cells that could be turned into a road. Specifically, the fish shop\u2019s cell is a road from the beginning, so it remains unchanged; particularly, the shop is not destroyed by the front kick.\n\nSample Input 4\n\n20 20\r\n####################\r\n##...##....###...###\r\n#.....#.....#.....##\r\n#..#..#..#..#..#..##\r\n#..#..#....##..#####\r\n#.....#.....#..#####\r\n#.....#..#..#..#..##\r\n#..#..#.....#.....##\r\n#..#..#....###...###\r\n####################\r\n####################\r\n##..#..##...###...##\r\n##..#..#.....#.....#\r\n##..#..#..#..#..#..#\r\n##..#..#..#..#..#..#\r\n##.....#..#..#..#..#\r\n###....#..#..#..#..#\r\n#####..#.....#.....#\r\n#####..##...###...##\r\n####################\r\n3 3 18 18\n\nSample Output 4\n\n3\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\nExecuted evidence disproved the program. Re-derive a general algorithm from the complete statement and constraints. Do not patch, fingerprint, or special-case the failing input. Return only one complete raw Python 3 program without Markdown, fences, or explanation.\nExecuted input:\n10 10\n..........\n#########.\n#.......#.\n#..####.#.\n##....#.#.\n#####.#.#.\n.##.#.#.#.\n###.#.#.#.\n###.#.#.#.\n#.....#...\n1 1 7 1\n\nProgram output:\n3\nTrusted expected output (published sample):\n1", "response": "import sys\nfrom collections import deque\nfrom array import array\n\ndef main():\n    input = sys.stdin.buffer.readline\n\n    H, W = map(int, input().split())\n    grid = [input().strip() for _ in range(H)]\n    A, B, C, D = map(int, input().split())\n    start = (A - 1) * W + (B - 1)\n    goal = (C - 1) * W + (D - 1)\n\n    n = H * W\n    inf = 10**9\n    dist = array('i', [inf]) * n\n    dist[start] = 0\n    q = deque([start])\n\n    while q:\n        v = q.popleft()\n        d = dist[v]\n        r, c = divmod(v, W)\n\n        for dr, dc in ((-1, 0), (1, 0), (0, -1), (0, 1)):\n            r1 = r + dr\n            c1 = c + dc\n\n            if 0 <= r1 < H and 0 <= c1 < W:\n                u1 = r1 * W + c1\n                if grid[r1][c1] == 46:\n                    if dist[u1] > d:\n                        dist[u1] = d\n                        q.appendleft(u1)\n                else:\n                    if dist[u1] > d + 1:\n                        dist[u1] = d + 1\n                        q.append(u1)\n\n                r2 = r + 2 * dr\n                c2 = c + 2 * dc\n                if 0 <= r2 < H and 0 <= c2 < W:\n                    u2 = r2 * W + c2\n                    if dist[u2] > d + 1:\n                        dist[u2] = d + 1\n                        q.append(u2)\n\n    print(dist[goal])\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.003215725, "tokens_in": 1328, "tokens_out": 5083, "latency_s": 66.209}]