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+[{"task_id": "mmlu-2666", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Which of the following mental disorders is most prevalent in the world?\nA) Bipolar disorder\nB) Schizophrenia\nC) Alcohol use disorders\nD) Anxiety disorders\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": 3.6e-05, "tokens_in": 72, "tokens_out": 48, "latency_s": 3.032}, {"task_id": "mmlu-717", "model": "openai/gpt-5.6-luna", "prompt": "[MMLU] Alterations in which neurotransmitters in the brain by pharmacological agents has been shown to influence fatigue development?\nA) Acetyl choline and noradrenaline.\nB) Dopamine and acetyl choline.\nC) Glutamate and serotonin.\nD) Dopamine and serotonin.\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": 7.429999999999999e-05, "tokens_in": 95, "tokens_out": 108, "latency_s": 2.401}, {"task_id": "gsm8k-1146", "model": "openai/gpt-5.6-luna", "prompt": "Adam has $100 and wants to spend it to open a rock stand. He can buy rocks for $5 each and sell them for $7 each. If he invests all his money in the rock stand but only sells 60% of his inventory, how much money does he lose?\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 170566)", "response": "1. He buys \\(100 \\div 5 = 20\\) rocks.\n2. He sells \\(20 \\times 60\\% = 12\\) rocks.\n3. He earns \\(12 \\times 7 = 84\\) dollars.\n4. His loss is \\(100 - 84 = 16\\) dollars.\n\n16", "cost_usd": 0.0001642, "tokens_in": 100, "tokens_out": 257, "latency_s": 2.837}, {"task_id": "gsm8k-394", "model": "openai/gpt-5.6-luna", "prompt": "Wendy wants to place 20 more than double the number of books in a shelving system with 6 rows and 6 columns. How many books will she need to carry to complete her task?\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 536336)", "response": "A shelving system with 6 rows and 6 columns holds:\n\n6 \u00d7 6 = 36 books\n\nDouble the number:\n\n2 \u00d7 36 = 72 books\n\nAdd 20 more:\n\n72 + 20 = 92\n\n92", "cost_usd": 7.180000000000001e-05, "tokens_in": 82, "tokens_out": 106, "latency_s": 2.452}, {"task_id": "lcb-abc400_a", "model": "openai/gpt-5.6-luna", "prompt": "In the ceremony commemorating ABC400, we want to arrange 400 people in a rectangular formation of A rows and B columns without any gaps.\nYou are given a positive integer A. Print the value of a positive integer B for which such an arrangement is possible. If there is no such positive integer B, print -1.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA\n\nOutput\n\nPrint the value of B or -1 as specified by the problem statement.\n\nConstraints\n\n\n- A is an integer between 1 and 400, inclusive.\n\nSample Input 1\n\n10\n\nSample Output 1\n\n40\r\n\nWe can arrange 400 people in 10 rows and 40 columns.\n\nSample Input 2\n\n11\n\nSample Output 2\n\n-1\n\nSample Input 3\n\n400\n\nSample Output 3\n\n1\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\ntokens = sys.stdin.buffer.read().split()\na = int(tokens[0])\nout = [str(400 // a if 400 % a == 0 else -1)]\nsys.stdout.write(\"\\n\".join(out))", "cost_usd": 0.0001048, "tokens_in": 412, "tokens_out": 106, "latency_s": 2.353}, {"task_id": "lcb-arc191_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string S of length N and a string T of length M, both consisting of digits from 1 to 9.\nYou will perform the following operation for k=1,2,\\ldots,M in order:\n\n- Choose an integer i such that 1 \\le i \\le N. Then, replace the i-th character of S with the k-th character of T.\n\nFind the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nS\nT\n\nOutput\n\nPrint the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nConstraints\n\n\n- 1 \\le N,M \\le 10^6\n- N and M are integers.\n- S is a string of length N consisting of digits from 1 through 9.\n- T is a string of length M consisting of digits from 1 through 9.\n\nSample Input 1\n\n3 3\n191\n325\n\nSample Output 1\n\n593\n\nThe following sequence of operations is optimal:\n\n- For k=1: Choose i=3. Then, S = 193.\n- For k=2: Choose i=1. Then, S = 293.\n- For k=3: Choose i=1. Then, S = 593.\n\nIn this case, the value of S interpreted as an integer is 593, which is the maximum.\n\nSample Input 2\n\n3 9\n191\n998244353\n\nSample Output 2\n\n993\n\nSample Input 3\n\n11 13\n31415926535\n2718281828459\n\nSample Output 3\n\n98888976555\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()\nn = int(data[0])\nm = int(data[1])\ns = list(data[2].decode())\nt = data[3].decode()\n\ncounts = [0] * 10\nfor c in t[:-1]:\n    counts[ord(c) - 48] += 1\n\nfor i in range(n):\n    cur = ord(s[i]) - 48\n    d = 9\n    while d > cur and counts[d] == 0:\n        d -= 1\n    if d > cur:\n        s[i] = chr(48 + d)\n        counts[d] -= 1\n\nmandatory = ord(t[-1]) - 48\nimprove = -1\nfor i, c in enumerate(s):\n    if mandatory > ord(c) - 48:\n        improve = i\n        break\n\nif improve != -1:\n    s[improve] = chr(48 + mandatory)\nelse:\n    s[-1] = chr(48 + mandatory)\n\nsys.stdout.write(''.join(s))", "cost_usd": 0.0012362, "tokens_in": 596, "tokens_out": 1961, "latency_s": 20.171}, {"task_id": "lcb-arc191_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string S of length N and a string T of length M, both consisting of digits from 1 to 9.\nYou will perform the following operation for k=1,2,\\ldots,M in order:\n\n- Choose an integer i such that 1 \\le i \\le N. Then, replace the i-th character of S with the k-th character of T.\n\nFind the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nS\nT\n\nOutput\n\nPrint the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nConstraints\n\n\n- 1 \\le N,M \\le 10^6\n- N and M are integers.\n- S is a string of length N consisting of digits from 1 through 9.\n- T is a string of length M consisting of digits from 1 through 9.\n\nSample Input 1\n\n3 3\n191\n325\n\nSample Output 1\n\n593\n\nThe following sequence of operations is optimal:\n\n- For k=1: Choose i=3. Then, S = 193.\n- For k=2: Choose i=1. Then, S = 293.\n- For k=3: Choose i=1. Then, S = 593.\n\nIn this case, the value of S interpreted as an integer is 593, which is the maximum.\n\nSample Input 2\n\n3 9\n191\n998244353\n\nSample Output 2\n\n993\n\nSample Input 3\n\n11 13\n31415926535\n2718281828459\n\nSample Output 3\n\n98888976555\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.\n\nPrevious attempts were WRONG on these inputs \u2014 use a different approach and make sure you handle them:\ninput: 3 3 191 325 -> expected 593", "response": "import sys\n\ndata = sys.stdin.buffer.read().split()\nn = int(data[0])\nm = int(data[1])\ns = data[2]\nt = data[3]\n\ncounts = [0] * 10\nfor b in t[:-1]:\n    counts[b - 48] += 1\n\nmandatory = t[-1] - 48\nused = False\nans = []\n\nfor b in s:\n    cur = b - 48\n    if used:\n        d = 9\n        while d > cur and counts[d] == 0:\n            d -= 1\n        if d > cur:\n            counts[d] -= 1\n            ans.append(chr(d + 48))\n        else:\n            ans.append(chr(cur + 48))\n    else:\n        d = 9\n        while d > cur and counts[d] == 0:\n            d -= 1\n        regular = d if counts[d] else 0\n\n        if mandatory >= cur and mandatory >= regular:\n            ans.append(chr(mandatory + 48))\n            used = True\n        elif regular > cur:\n            counts[regular] -= 1\n            ans.append(chr(regular + 48))\n        else:\n            ans.append(chr(cur + 48))\n\nif not used:\n    ans[-1] = chr(mandatory + 48)\n\nsys.stdout.write(''.join(ans))", "cost_usd": 0.0031942999999999997, "tokens_in": 629, "tokens_out": 5219, "latency_s": 62.791}, {"task_id": "lcb-arc191_a", "model": "openai/gpt-5.6-luna", "prompt": "You are given a string S of length N and a string T of length M, both consisting of digits from 1 to 9.\nYou will perform the following operation for k=1,2,\\ldots,M in order:\n\n- Choose an integer i such that 1 \\le i \\le N. Then, replace the i-th character of S with the k-th character of T.\n\nFind the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nS\nT\n\nOutput\n\nPrint the maximum possible value of the resulting string S interpreted as an integer after performing the M operations.\n\nConstraints\n\n\n- 1 \\le N,M \\le 10^6\n- N and M are integers.\n- S is a string of length N consisting of digits from 1 through 9.\n- T is a string of length M consisting of digits from 1 through 9.\n\nSample Input 1\n\n3 3\n191\n325\n\nSample Output 1\n\n593\n\nThe following sequence of operations is optimal:\n\n- For k=1: Choose i=3. Then, S = 193.\n- For k=2: Choose i=1. Then, S = 293.\n- For k=3: Choose i=1. Then, S = 593.\n\nIn this case, the value of S interpreted as an integer is 593, which is the maximum.\n\nSample Input 2\n\n3 9\n191\n998244353\n\nSample Output 2\n\n993\n\nSample Input 3\n\n11 13\n31415926535\n2718281828459\n\nSample Output 3\n\n98888976555\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\nsys.setrecursionlimit(10**7)\n\ndef main():\n    data = sys.stdin.read().split()\n    if not data:\n        return\n\n    n = int(data[0])\n    m = int(data[1])\n    s = list(data[2])\n    t = data[3]\n\n    best = None\n\n    def dfs(k):\n        nonlocal best\n        if k == m:\n            current = ''.join(s)\n            if best is None or current > best:\n                best = current\n            return\n\n        digit = t[k]\n        for i in range(n):\n            old = s[i]\n            s[i] = digit\n            dfs(k + 1)\n            s[i] = old\n\n    dfs(0)\n    sys.stdout.write(best + \"\\n\")\n\nif __name__ == \"__main__\":\n    main()\n```\n\n```generator\nimport sys\nimport random\n\ndef main():\n    seed = int(sys.argv[1])\n    size = int(sys.argv[2])\n    random.seed(seed)\n\n    if size == 2:\n        print(\"1 1\")\n        print(\"1\")\n        print(\"1\")\n        return\n\n    n = min(10**6, max(1, size - 1))\n    m = min(10**6, max(1, size))\n\n    pool = \"111199995555678234\"\n    s = ''.join(random.choice(pool) for _ in range(n))\n    t = ''.join(random.choice(pool) for _ in range(m))\n\n    print(n, m)\n    print(s)\n    print(t)\n\nif __name__ == \"__main__\":\n    main()\n```", "cost_usd": 0.0005574999999999998, "tokens_in": 523, "tokens_out": 842, "latency_s": 7.808}]