{"problem":{"name":"Problem Scores","description":{"content":"$N$ problems have been chosen by the judges, now it's time to assign scores to them! Problem $i$ must get an integer score $A_i$ between $1$ and $N$, inclusive. The problems have already been sorted b","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc041_d"},"statements":[{"statement_type":"Markdown","content":"$N$ problems have been chosen by the judges, now it's time to assign scores to them!\nProblem $i$ must get an integer score $A_i$ between $1$ and $N$, inclusive. The problems have already been sorted by difficulty: $A_1 \\le A_2 \\le \\ldots \\le A_N$ must hold. Different problems can have the same score, though.\nBeing an ICPC fan, you want contestants who solve more problems to be ranked higher. That's why, for any $k$ ($1 \\le k \\le N-1$), you want the sum of scores of any $k$ problems to be strictly less than the sum of scores of any $k+1$ problems.\nHow many ways to assign scores do you have? Find this number modulo the given prime $M$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 5000$\n*   $9 \\times 10^8 < M < 10^9$\n*   $M$ is a prime.\n*   All input values are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc041_d","tags":[],"sample_group":[["2 998244353","3\n\nThe possible assignments are $(1, 1)$, $(1, 2)$, $(2, 2)$."],["3 998244353","7\n\nThe possible assignments are $(1, 1, 1)$, $(1, 2, 2)$, $(1, 3, 3)$, $(2, 2, 2)$, $(2, 2, 3)$, $(2, 3, 3)$, $(3, 3, 3)$."],["6 966666661","66"],["96 925309799","83779"]],"created_at":"2026-03-03 11:01:14"}}