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+[{"task_id": "mmlu-6851", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] In building a linear regression model for a particular data set, you observe the coefficient of one of the features having a relatively high negative value. This suggests that\nA) This feature has a strong effect on the model (should be retained)\nB) This feature does not have a strong effect on the model (should be ignored)\nC) It is not possible to comment on the importance of this feature without additional information\nD) Nothing can be determined.\n\nAnswer with the letter only.\n\nThink step by step about each option, then end with exactly: ANSWER: <letter>", "response": "ANSWER: C", "cost_usd": 6.6e-05, "tokens_in": 126, "tokens_out": 89, "latency_s": 3.522}, {"task_id": "mmlu-4407", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] A solid is cut out of a sphere of radius 2 by two parallel planes each 1 unit from the center. The volume of this solid is\nA) 8\u03c0\nB) 32\u03c0/3\nC) 25\u03c0/3\nD) 22\u03c0/3\n\nAnswer with the letter only.\n\nThink step by step about each option, then end with exactly: ANSWER: <letter>", "response": "ANSWER: D", "cost_usd": 0.00010319999999999999, "tokens_in": 96, "tokens_out": 156, "latency_s": 2.198}, {"task_id": "gsm8k-750", "model": "openai/gpt-5.6-luna", "prompt": "Candy has a chair rental business. During the weekdays, 60 chairs are rented each day; but during weekends, 100 chairs are rented each day. If this continues, how many chairs in total will Candy be able to rent out in two 4-week months?\n\nReason step by step, then give the final answer as a single number.\n\nReason step by step, then end with the final answer as a single number.\n\n(ref 852102)", "response": "1. Each week has 5 weekdays and 2 weekend days.\n2. Weekday rentals: \\(5 \\times 60 = 300\\) chairs.\n3. Weekend rentals: \\(2 \\times 100 = 200\\) chairs.\n4. Total per week: \\(300 + 200 = 500\\) chairs.\n5. Two 4-week months contain \\(8\\) weeks.\n6. Total rentals: \\(8 \\times 500 = 4000\\).\n\n4000", "cost_usd": 0.00011099999999999999, "tokens_in": 96, "tokens_out": 169, "latency_s": 2.807}, {"task_id": "gsm8k-551", "model": "openai/gpt-5.6-luna", "prompt": "Carly wants to treat her friends. She orders five hamburgers at $4 each, ten packs of potato fries at $0.30 each pack, and five cans of fruit drinks at $2 each can.  How much change does Carly get back if she gives one fifty-dollar bill?\n\nReason step by step, then give the final answer as a single number.\n\nReason step by step, then end with the final answer as a single number.\n\n(ref 823027)", "response": "Five hamburgers: \\(5 \\times \\$4 = \\$20\\)\n\nTen packs of fries: \\(10 \\times \\$0.30 = \\$3\\)\n\nFive fruit drinks: \\(5 \\times \\$2 = \\$10\\)\n\nTotal cost: \\(\\$20 + \\$3 + \\$10 = \\$33\\)\n\nChange: \\(\\$50 - \\$33 = \\$17\\)\n\n17", "cost_usd": 8.330000000000002e-05, "tokens_in": 101, "tokens_out": 122, "latency_s": 2.534}, {"task_id": "lcb-abc399_b", "model": "openai/gpt-5.6-luna", "prompt": "N people labeled from 1 to N participated in a certain contest. The score of person i (1 \\leq i \\leq N) was P_i.\nIn this contest, the rank of each of the N people is determined by the following procedure:\n\n- Prepare a variable r, and initialize r = 1. Initially, the ranks of the N people are all undetermined.\n- Repeat the following operation until the ranks of all N people are determined:\n- Let x be the maximum score among the people whose ranks are currently undetermined, and let k be the number of people whose score is x. Determine the rank of those k people with score x to be r, and then add k to r.\n\n\n\nPrint the rank of each of the N people.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\dots P_N\n\nOutput\n\nPrint N lines. The i-th line (1 \\leq i \\leq N) should contain the rank of person i as an integer.\n\nConstraints\n\n\n- 1\\leq N \\leq 100\n- 1\\leq P_i \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n4\r\n3 12 9 9\n\nSample Output 1\n\n4\r\n1\r\n2\r\n2\r\n\nThe ranks of the N\\ (=4) people are determined as follows:\n\n- Prepare a variable r and initialize r=1. At first, the ranks of all 4 people are undetermined.\n- Currently, persons 1, 2, 3, 4 have undetermined ranks. The maximum score among them is P_2\\ (=12). Therefore, determine the rank of person 2 to be r\\ (=1), and then add 1 to r, making r=2.\n- Currently, persons 1, 3, 4 have undetermined ranks. The maximum score among them is P_3=P_4\\ (=9). Therefore, determine the ranks of persons 3 and 4 to be r\\ (=2), and then add 2 to r, making r=4.\n- Currently, person 1 has an undetermined rank. The maximum score among them is P_1\\ (=3). Therefore, determine the rank of person 1 to be r\\ (=4), and then add 1 to r, making r=5.\n- The ranks of all 4 people are now determined, so the process ends.\n\nSample Input 2\n\n3\r\n3 9 6\n\nSample Output 2\n\n3\r\n1\r\n2\n\nSample Input 3\n\n4\r\n100 100 100 100\n\nSample Output 3\n\n1\r\n1\r\n1\r\n1\n\nSample Input 4\n\n8\r\n87 87 87 88 41 38 41 38\n\nSample Output 4\n\n2\r\n2\r\n2\r\n1\r\n5\r\n7\r\n5\r\n7\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\nSolve this competitive-programming problem in Python 3. Read all of stdin at once with sys.stdin.buffer.read().split() and index across tokens; build output in a list and emit it with one write at the end. Check the constraint block and pick an algorithm whose running time stays under ~1e8 steps at the largest allowed input. Return ONLY raw complete Python 3 source \u2014 no Markdown fences, no prose, no comments.\n\nOUTPUT FORMAT: this judge compares printed output EXACTLY, token for token, even when the statement promises a numeric tolerance, and the hidden tests may not use the same precision as the statement's worked examples. Apply BOTH: (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; (2) for every other input print floats at a fixed width with format(x, '.12f'). Never pin an input that is not a worked example; compute those normally.", "response": "import sys\n\ndata = list(map(int, sys.stdin.buffer.read().split()))\nn = data[0]\nscores = data[1:1 + n]\n\nrank = {}\ncurrent = 1\nfor score in sorted(set(scores), reverse=True):\n    rank[score] = current\n    current += scores.count(score)\n\nout = [str(rank[score]) for score in scores]\nsys.stdout.write(\"\\n\".join(out))", "cost_usd": 0.00021049999999999997, "tokens_in": 851, "tokens_out": 209, "latency_s": 3.762}, {"task_id": "lcb-abc399_b", "model": "openai/gpt-5.6-luna", "prompt": "N people labeled from 1 to N participated in a certain contest. The score of person i (1 \\leq i \\leq N) was P_i.\nIn this contest, the rank of each of the N people is determined by the following procedure:\n\n- Prepare a variable r, and initialize r = 1. Initially, the ranks of the N people are all undetermined.\n- Repeat the following operation until the ranks of all N people are determined:\n- Let x be the maximum score among the people whose ranks are currently undetermined, and let k be the number of people whose score is x. Determine the rank of those k people with score x to be r, and then add k to r.\n\n\n\nPrint the rank of each of the N people.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\dots P_N\n\nOutput\n\nPrint N lines. The i-th line (1 \\leq i \\leq N) should contain the rank of person i as an integer.\n\nConstraints\n\n\n- 1\\leq N \\leq 100\n- 1\\leq P_i \\leq 100\n- All input values are integers.\n\nSample Input 1\n\n4\r\n3 12 9 9\n\nSample Output 1\n\n4\r\n1\r\n2\r\n2\r\n\nThe ranks of the N\\ (=4) people are determined as follows:\n\n- Prepare a variable r and initialize r=1. At first, the ranks of all 4 people are undetermined.\n- Currently, persons 1, 2, 3, 4 have undetermined ranks. The maximum score among them is P_2\\ (=12). Therefore, determine the rank of person 2 to be r\\ (=1), and then add 1 to r, making r=2.\n- Currently, persons 1, 3, 4 have undetermined ranks. The maximum score among them is P_3=P_4\\ (=9). Therefore, determine the ranks of persons 3 and 4 to be r\\ (=2), and then add 2 to r, making r=4.\n- Currently, person 1 has an undetermined rank. The maximum score among them is P_1\\ (=3). Therefore, determine the rank of person 1 to be r\\ (=4), and then add 1 to r, making r=5.\n- The ranks of all 4 people are now determined, so the process ends.\n\nSample Input 2\n\n3\r\n3 9 6\n\nSample Output 2\n\n3\r\n1\r\n2\n\nSample Input 3\n\n4\r\n100 100 100 100\n\nSample Output 3\n\n1\r\n1\r\n1\r\n1\n\nSample Input 4\n\n8\r\n87 87 87 88 41 38 41 38\n\nSample Output 4\n\n2\r\n2\r\n2\r\n1\r\n5\r\n7\r\n5\r\n7\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\nNow write TWO programs and nothing else. FIRST a REFERENCE solution that is correct by construction and may be arbitrarily slow (brute force / full simulation); do NOT reuse the idea from the fast solution \u2014 it must be able to disagree. SECOND a GENERATOR taking two argv ints (seed, size): call random.seed(seed) and print ONE valid random input in the exact stdin format, obeying every constraint; at size 2 emit the smallest legal input, larger sizes proportionally bigger, with repeats and extreme values. Output exactly two fenced blocks:\n```reference\n<prog>\n```\n```generator\n<prog>\n```", "response": "```reference\nimport sys\n\ndef main():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    n = data[0]\n    scores = data[1:1 + n]\n\n    undetermined = [True] * n\n    ranks = [0] * n\n    r = 1\n    remaining = n\n\n    while remaining:\n        maximum = None\n        for i in range(n):\n            if undetermined[i]:\n                if maximum is None or scores[i] > maximum:\n                    maximum = scores[i]\n\n        count = 0\n        for i in range(n):\n            if undetermined[i] and scores[i] == maximum:\n                count += 1\n\n        for i in range(n):\n            if undetermined[i] and scores[i] == maximum:\n                ranks[i] = r\n                undetermined[i] = False\n\n        remaining -= count\n        r += count\n\n    sys.stdout.write(\"\\n\".join(map(str, ranks)))\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 = int(sys.argv[2])\n    random.seed(seed)\n\n    n = max(1, size - 1)\n\n    if size == 2:\n        scores = [1]\n    else:\n        choices = [1, 2, 3, 50, 98, 99, 100]\n        scores = [random.choice(choices) for _ in range(n)]\n        if n >= 2:\n            scores[0] = 1\n            scores[1] = 100\n        if n >= 3:\n            scores[2] = random.choice([1, 100])\n\n    print(n)\n    print(*scores)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0003736, "tokens_in": 778, "tokens_out": 493, "latency_s": 3.352}, {"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\nSolve this competitive-programming problem in Python 3. Read all of stdin at once with sys.stdin.buffer.read().split() and index across tokens; build output in a list and emit it with one write at the end. Check the constraint block and pick an algorithm whose running time stays under ~1e8 steps at the largest allowed input. Return ONLY raw complete Python 3 source \u2014 no Markdown fences, no prose, no comments.\n\nOUTPUT FORMAT: this judge compares printed output EXACTLY, token for token, even when the statement promises a numeric tolerance, and the hidden tests may not use the same precision as the statement's worked examples. Apply BOTH: (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; (2) for every other input print floats at a fixed width with format(x, '.12f'). Never pin an input that is not a worked example; compute those normally.", "response": "import sys\n\ndata = sys.stdin.buffer.read().split()\nidx = 0\n\nn = int(data[idx])\nidx += 1\nm = int(data[idx])\nidx += 1\n\na = list(map(int, data[idx:idx + n]))\nidx += n\nb = list(map(int, data[idx:idx + m]))\n\nearly = [-1] * m\nj = 0\nfor i, value in enumerate(a):\n    if j < m and value == b[j]:\n        early[j] = i\n        j += 1\n\nlate = [-1] * m\nj = m - 1\nfor i in range(n - 1, -1, -1):\n    if j >= 0 and a[i] == b[j]:\n        late[j] = i\n        j -= 1\n\nout = []\nif j >= 0:\n    out.append(\"No\")\nelif early == late:\n    out.append(\"No\")\nelse:\n    out.append(\"Yes\")\n\nsys.stdout.write(\"\\n\".join(out))", "cost_usd": 0.0005021, "tokens_in": 605, "tokens_out": 736, "latency_s": 6.925}, {"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\nNow write TWO programs and nothing else. FIRST a REFERENCE solution that is correct by construction and may be arbitrarily slow (brute force / full simulation); do NOT reuse the idea from the fast solution \u2014 it must be able to disagree. SECOND a GENERATOR taking two argv ints (seed, size): call random.seed(seed) and print ONE valid random input in the exact stdin format, obeying every constraint; at size 2 emit the smallest legal input, larger sizes proportionally bigger, with repeats and extreme values. Output exactly two fenced blocks:\n```reference\n<prog>\n```\n```generator\n<prog>\n```", "response": "```reference\nimport sys\nimport itertools\n\ndef main():\n    data = list(map(int, sys.stdin.buffer.read().split()))\n    if not data:\n        return\n\n    n, m = data[0], data[1]\n    a = data[2:2 + n]\n    b = data[2 + n:2 + n + m]\n\n    count = 0\n    for indices in itertools.combinations(range(n), m):\n        if all(a[i] == b[j] for j, i in enumerate(indices)):\n            count += 1\n            if count >= 2:\n                print(\"Yes\")\n                return\n\n    print(\"No\")\n\nif __name__ == \"__main__\":\n    main()\n```\n\n```generator\nimport sys\nimport random\n\nseed = int(sys.argv[1])\nsize = int(sys.argv[2])\nrandom.seed(seed)\n\nn = max(1, size - 1)\nm = random.randint(1, n)\n\npool = [\n    1,\n    2,\n    3,\n    10**9,\n    10**9 - 1,\n    random.randint(1, 10**9),\n]\n\na = [random.choice(pool) for _ in range(n)]\nb = [random.choice(pool) for _ in range(m)]\n\nprint(n, m)\nprint(*a)\nprint(*b)\n```", "cost_usd": 0.0003304, "tokens_in": 532, "tokens_out": 462, "latency_s": 5.47}]