{"problem":{"name":"Multiset Mean","description":{"content":"Given positive integers $N, K$ and $M$, solve the following problem for every integer $x$ between $1$ and $N$ (inclusive): *   Find the number, modulo $M$, of non-empty multisets containing between $","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":4000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc104_d"},"statements":[{"statement_type":"Markdown","content":"Given positive integers $N, K$ and $M$, solve the following problem for every integer $x$ between $1$ and $N$ (inclusive):\n\n*   Find the number, modulo $M$, of non-empty multisets containing between $0$ and $K$ (inclusive) instances of each of the integers $1, 2, 3 \\cdots, N$ such that the average of the elements is $x$.\n\n## Constraints\n\n*   $1 \\leq N, K \\leq 100$\n*   $10^8 \\leq M \\leq 10^9 + 9$\n*   $M$ is prime.\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc104_d","tags":[],"sample_group":[["3 1 998244353","1\n3\n1\n\nConsider non-empty multisets containing between $0$ and $1$ instance(s) of each of the integers between $1$ and $3$. Among them, there are:\n\n*   one multiset such that the average of the elements is $k = 1$: ${1}$;\n*   three multisets such that the average of the elements is $k = 2$: ${2}, {1, 3}, {1, 2, 3}$;\n*   one multiset such that the average of the elements is $k = 3$: ${3}$."],["1 2 1000000007","2\n\nConsider non-empty multisets containing between $0$ and $2$ instances of each of the integers between $1$ and $1$. Among them, there are:\n\n*   two multisets such that the average of the elements is $k = 1$: ${1}, {1, 1}$."],["10 8 861271909","8\n602\n81827\n4054238\n41331779\n41331779\n4054238\n81827\n602\n8"]],"created_at":"2026-03-03 11:01:14"}}