{"problem":{"name":"Count Multiset","description":{"content":"Given are positive integers $N$ and $M$. For each $k=1,2,\\ldots,N$, find the following number and print it modulo $998244353$. *   The number of multisets $A$ containing $k$ positive integers that sa","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc221_h"},"statements":[{"statement_type":"Markdown","content":"Given are positive integers $N$ and $M$.\nFor each $k=1,2,\\ldots,N$, find the following number and print it modulo $998244353$.\n\n*   The number of multisets $A$ containing $k$ positive integers that satisfy both of the following conditions:\n    *   the sum of the elements of $A$ is $N$;\n    *   for every positive integer $x$, $A$ contains at most $M$ occurrences of $x$.\n\n## Constraints\n\n*   $1 \\leq M \\leq N \\leq 5000$\n*   All values in input 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":"abc221_h","tags":[],"sample_group":[["4 2","1\n2\n1\n0\n\n*   For $k=1$, there is one multiset $A$ that satisfies the conditions: ${4}$.\n*   For $k=2$, there are two multisets $A$ that satisfy the conditions: ${1,3}$ and ${2,2}$.\n*   For $k=3$, there is one multiset $A$ that satisfies the conditions: ${1,1,2}$.\n*   For $k=4$, there is no multiset $A$ that satisfies the conditions."],["7 7","1\n3\n4\n3\n2\n1\n1"]],"created_at":"2026-03-03 11:01:14"}}