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+[{"task_id": "mmlu-12959", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] The risk of withdrawal delirium is greatest following discontinuation of which of the following substances\nA) Cocaine\nB) LSD\nC) Phenobarbital\nD) Heroin\n\nAnswer with the letter only.", "response": "C", "cost_usd": 8.5e-06, "tokens_in": 55, "tokens_out": 5, "latency_s": 2.125}, {"task_id": "mmlu-2760", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A form of species interaction in which one of the species benefits while the other is unaffected is called\nA) parasitism.\nB) mutualism.\nC) commensalism.\nD) symbiosis.\n\nAnswer with the letter only.", "response": "C", "cost_usd": 8.999999999999999e-06, "tokens_in": 60, "tokens_out": 5, "latency_s": 0.888}, {"task_id": "gsm8k-409", "model": "openai/gpt-5.6-luna", "prompt": "Carolyn works for a delivery service company that hires on a contract basis. In May, they hired 40 employees, paying each employee $15 per hour for a 40-hour workweek. In June, 1/4 of the employees' contracts expired. Calculate the total amount of money the company paid to the employees in the two months.\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": "1. Weekly pay per employee: \\(15 \\times 40 = 600\\).\n2. May pay: \\(40 \\times 600 \\times 4 = 96{,}000\\).\n3. Employees remaining in June: \\(40 \\times \\frac{3}{4} = 30\\).\n4. June pay: \\(30 \\times 600 \\times 4 = 72{,}000\\).\n5. Total paid: \\(96{,}000 + 72{,}000 = 168{,}000\\).\n\n168000", "cost_usd": 0.000165, "tokens_in": 120, "tokens_out": 255, "latency_s": 4.66}, {"task_id": "gsm8k-432", "model": "openai/gpt-5.6-luna", "prompt": "Prince Thaddeus slew 100 dragons with his mighty sword, while Prince Arthur, using a spear, slew three quarters as many dragons as Prince Thaddeus.  Using a rusty iron axe, Prince Walter slew twice as many dragons as Prince Arthur.  But Prince Bruce, having forgot his sword at home, slew one-fifth as many dragons as Prince Walter using a nail file.  How many Dragons has Prince Bruce slain?\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": "Prince Arthur slew \\( \\frac{3}{4} \\times 100 = 75\\) dragons.\n\nPrince Walter slew \\(2 \\times 75 = 150\\) dragons.\n\nPrince Bruce slew \\( \\frac{1}{5} \\times 150 = 30\\) dragons.\n\n30", "cost_usd": 8.389999999999998e-05, "tokens_in": 137, "tokens_out": 117, "latency_s": 3.241}, {"task_id": "lcb-abc389_b", "model": "openai/gpt-5.6-luna", "prompt": "You are given an integer X not less than 2.\nFind the positive integer N such that N! = X.\nHere, N! denotes the factorial of N, and it is guaranteed that there is exactly one such N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nX\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 2 \\leq X \\leq 3 \\times 10^{18}\n- There is exactly one positive integer N such that N!=X.\n- All input values are integers.\n\nSample Input 1\n\n6\n\nSample Output 1\n\n3\r\n\nFrom 3!=3\\times2\\times1=6, print 3.\n\nSample Input 2\n\n2432902008176640000\n\nSample Output 2\n\n20\r\n\nFrom 20!=2432902008176640000, print 20.\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\n\nx = int(sys.stdin.readline())\nn = 1\nfactorial = 1\n\nwhile factorial < x:\n    n += 1\n    factorial *= n\n\nprint(n)", "cost_usd": 5.9599999999999985e-05, "tokens_in": 332, "tokens_out": 44, "latency_s": 1.593}, {"task_id": "lcb-abc389_b", "model": "openai/gpt-5.6-luna", "prompt": "You are given an integer X not less than 2.\nFind the positive integer N such that N! = X.\nHere, N! denotes the factorial of N, and it is guaranteed that there is exactly one such N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nX\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 2 \\leq X \\leq 3 \\times 10^{18}\n- There is exactly one positive integer N such that N!=X.\n- All input values are integers.\n\nSample Input 1\n\n6\n\nSample Output 1\n\n3\r\n\nFrom 3!=3\\times2\\times1=6, print 3.\n\nSample Input 2\n\n2432902008176640000\n\nSample Output 2\n\n20\r\n\nFrom 20!=2432902008176640000, print 20.\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\nx = int(sys.stdin.readline())\nfactorial = 1\nn = 1\n\nwhile factorial < x:\n    n += 1\n    factorial *= n\n\nif factorial == x:\n    print(n)\n```\n\n```generator\nimport random\nimport sys\nimport math\n\nseed = int(sys.argv[1])\nsize = int(sys.argv[2])\nrandom.seed(seed)\n\nmax_n = max(2, min(20, size + 2))\n\ncandidates = list(range(2, max_n + 1))\nif size <= 0:\n    n = 2\nelse:\n    families = [\n        candidates,\n        [2, max_n],\n        [2, 3, max_n],\n        candidates[::2],\n        candidates[1::2] or candidates,\n    ]\n    family = families[random.randrange(len(families))]\n    n = random.choice(family)\n\nprint(math.factorial(n))\n```", "cost_usd": 0.0003217, "tokens_in": 385, "tokens_out": 472, "latency_s": 5.592}, {"task_id": "lcb-abc388_d", "model": "openai/gpt-5.6-luna", "prompt": "On a certain planet, there are N aliens, all of whom are minors.\nThe i-th alien currently has A_i stones, and will become an adult exactly i years later.\nWhen someone becomes an adult on this planet, every adult who has at least one stone gives exactly one stone as a congratulatory gift to the alien who has just become an adult.\nFind how many stones each alien will have after N years.\nAssume that no new aliens will be born in the future.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nLet B_i be the number of stones owned by the i-th alien after N years. Print B_1, B_2, \\ldots, B_N in this order, separated by spaces.\n\nConstraints\n\n\n- 1 \\leq N \\leq 5 \\times 10^5\n- 0 \\leq A_i \\leq 5 \\times 10^5\n- All input values are integers.\n\nSample Input 1\n\n4\r\n5 0 9 3\n\nSample Output 1\n\n2 0 10 5\r\n\nLet C_i be the number of stones that the i-th alien has at a given time.\nInitially, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).\nAfter 1 year, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).\nAfter 2 years, (C_1, C_2, C_3, C_4) = (4, 1, 9, 3).\nAfter 3 years, (C_1, C_2, C_3, C_4) = (3, 0, 11, 3).\nAfter 4 years, (C_1, C_2, C_3, C_4) = (2, 0, 10, 5).\n\nSample Input 2\n\n5\r\n4 6 7 2 5\n\nSample Output 2\n\n0 4 7 4 9\n\nSample Input 3\n\n10\r\n2 9 1 2 0 4 6 7 1 5\n\nSample Output 3\n\n0 2 0 0 0 4 7 10 4 10\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\nimport heapq\n\ndef main():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    n = data[0]\n    a = data[1:]\n\n    heap = []\n    stored = [0] * n\n    offset = 0\n\n    for i in range(n):\n        while heap and heap[0] <= offset:\n            heapq.heappop(heap)\n\n        donors = len(heap)\n        offset += 1\n        value = a[i] + donors\n        stored[i] = value + offset\n        heapq.heappush(heap, stored[i])\n\n    result = [str(max(0, value - offset)) for value in stored]\n    sys.stdout.write(\" \".join(result))\n\nif __name__ == \"__main__\":\n    main()\n", "cost_usd": 0.0010993, "tokens_in": 673, "tokens_out": 1720, "latency_s": 21.281}, {"task_id": "lcb-abc388_d", "model": "openai/gpt-5.6-luna", "prompt": "On a certain planet, there are N aliens, all of whom are minors.\nThe i-th alien currently has A_i stones, and will become an adult exactly i years later.\nWhen someone becomes an adult on this planet, every adult who has at least one stone gives exactly one stone as a congratulatory gift to the alien who has just become an adult.\nFind how many stones each alien will have after N years.\nAssume that no new aliens will be born in the future.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nLet B_i be the number of stones owned by the i-th alien after N years. Print B_1, B_2, \\ldots, B_N in this order, separated by spaces.\n\nConstraints\n\n\n- 1 \\leq N \\leq 5 \\times 10^5\n- 0 \\leq A_i \\leq 5 \\times 10^5\n- All input values are integers.\n\nSample Input 1\n\n4\r\n5 0 9 3\n\nSample Output 1\n\n2 0 10 5\r\n\nLet C_i be the number of stones that the i-th alien has at a given time.\nInitially, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).\nAfter 1 year, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).\nAfter 2 years, (C_1, C_2, C_3, C_4) = (4, 1, 9, 3).\nAfter 3 years, (C_1, C_2, C_3, C_4) = (3, 0, 11, 3).\nAfter 4 years, (C_1, C_2, C_3, C_4) = (2, 0, 10, 5).\n\nSample Input 2\n\n5\r\n4 6 7 2 5\n\nSample Output 2\n\n0 4 7 4 9\n\nSample Input 3\n\n10\r\n2 9 1 2 0 4 6 7 1 5\n\nSample Output 3\n\n0 2 0 0 0 4 7 10 4 10\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    data = list(map(int, sys.stdin.buffer.read().split()))\n    if not data:\n        return\n\n    n = data[0]\n    c = data[1:1 + n]\n\n    for i in range(n):\n        donors = 0\n        for j in range(i):\n            if c[j] > 0:\n                c[j] -= 1\n                donors += 1\n        c[i] += donors\n\n    print(*c)\n\nif __name__ == \"__main__\":\n    main()\n```\n\n```generator\nimport random\nimport sys\n\ndef main():\n    if len(sys.argv) != 3:\n        raise SystemExit(\"usage: generator SEED SIZE\")\n\n    seed = int(sys.argv[1])\n    n = int(sys.argv[2])\n    if n < 1 or n > 500000:\n        raise SystemExit(\"SIZE must be between 1 and 500000\")\n\n    random.seed(seed)\n    mode = seed % 8\n    max_a = 500000\n\n    if mode == 0:\n        values = [0] * n\n        for _ in range(max(1, n // 3)):\n            values[random.randrange(n)] = random.choice([0, 1, 2, 500000])\n    elif mode == 1:\n        values = [random.choice([0, 1, 1, 2, 2, 3, 500000]) for _ in range(n)]\n    elif mode == 2:\n        values = [random.randrange(max_a + 1) for _ in range(n)]\n    elif mode == 3:\n        values = [random.choice([0, 1, 500000, random.randrange(10)]) for _ in range(n)]\n    elif mode == 4:\n        values = [min(max_a, i + random.choice([-1, 0, 1, 2])) for i in range(n)]\n    elif mode == 5:\n        values = [min(max_a, max(0, n - i + random.choice([-2, -1, 0, 1, 2])))\n                  for i in range(n)]\n    elif mode == 6:\n        pool = [0, 1, 2, n, max(0, n - 1), 500000, 499999]\n        values = [random.choice(pool) for _ in range(n)]\n    else:\n        values = []\n        for i in range(n):\n            r = random.random()\n            if r < 0.25:\n                values.append(0)\n            elif r < 0.5:\n                values.append(500000)\n            elif r < 0.75:\n                values.append(i % 7)\n            else:\n                values.append(random.randrange(max_a + 1))\n\n    print(n)\n    print(*values)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0009108, "tokens_in": 726, "tokens_out": 1397, "latency_s": 13.287}, {"task_id": "lcb-abc388_d", "model": "google/gemini-3.6-flash", "prompt": "On a certain planet, there are N aliens, all of whom are minors.\nThe i-th alien currently has A_i stones, and will become an adult exactly i years later.\nWhen someone becomes an adult on this planet, every adult who has at least one stone gives exactly one stone as a congratulatory gift to the alien who has just become an adult.\nFind how many stones each alien will have after N years.\nAssume that no new aliens will be born in the future.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nLet B_i be the number of stones owned by the i-th alien after N years. Print B_1, B_2, \\ldots, B_N in this order, separated by spaces.\n\nConstraints\n\n\n- 1 \\leq N \\leq 5 \\times 10^5\n- 0 \\leq A_i \\leq 5 \\times 10^5\n- All input values are integers.\n\nSample Input 1\n\n4\r\n5 0 9 3\n\nSample Output 1\n\n2 0 10 5\r\n\nLet C_i be the number of stones that the i-th alien has at a given time.\nInitially, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).\nAfter 1 year, (C_1, C_2, C_3, C_4) = (5, 0, 9, 3).\nAfter 2 years, (C_1, C_2, C_3, C_4) = (4, 1, 9, 3).\nAfter 3 years, (C_1, C_2, C_3, C_4) = (3, 0, 11, 3).\nAfter 4 years, (C_1, C_2, C_3, C_4) = (2, 0, 10, 5).\n\nSample Input 2\n\n5\r\n4 6 7 2 5\n\nSample Output 2\n\n0 4 7 4 9\n\nSample Input 3\n\n10\r\n2 9 1 2 0 4 6 7 1 5\n\nSample Output 3\n\n0 2 0 0 0 4 7 10 4 10\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\nIndependently derive a small-input reference program from the complete statement. Use direct simulation or exhaustive search rather than the intended efficient algorithm. Read the original input format and print the original output format. 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 one raw complete Python 3 program without Markdown or explanation.", "response": "import sys\n\n\ndef main():\n    input_data = sys.stdin.read().split()\n    if not input_data:\n        return\n    N = int(input_data[0])\n    A = [int(x) for x in input_data[1 : N + 1]]\n\n    diff = [0] * (N + 2)\n    curr_sum = 0\n    B = [0] * N\n\n    for i in range(N):\n        j = i + 1\n        curr_sum += diff[j]\n        S_j = A[i] + curr_sum\n        T_j = S_j + j\n\n        if j + 1 <= N:\n            diff[j + 1] += 1\n            limit = T_j + 1\n            if limit <= N:\n                diff[limit] -= 1\n\n        B[i] = max(0, S_j - (N - j))\n\n    print(*(B))\n\n\nif __name__ == \"__main__\":\n    main()", "cost_usd": 0.024709499999999995, "tokens_in": 676, "tokens_out": 6454, "latency_s": 30.407}]