{"problem":{"name":"Number of Multisets","description":{"content":"You are given two positive integers $N$ and $K$. How many multisets of rational numbers satisfy all of the following conditions? *   The multiset has exactly $N$ elements and the sum of them is equal","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc107_d"},"statements":[{"statement_type":"Markdown","content":"You are given two positive integers $N$ and $K$. How many multisets of rational numbers satisfy all of the following conditions?\n\n*   The multiset has exactly $N$ elements and the sum of them is equal to $K$.\n*   Each element of the multiset is one of $1, \\frac{1}{2}, \\frac{1}{4}, \\frac{1}{8}, \\dots$. In other words, each element can be represented as $\\frac{1}{2^i}\\ (i = 0,1,\\dots)$.\n\nThe answer may be large, so print it modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq K \\leq N \\leq 3000$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc107_d","tags":[],"sample_group":[["4 2","2\n\nThe following two multisets satisfy all of the given conditions:\n\n*   ${1, \\frac{1}{2}, \\frac{1}{4}, \\frac{1}{4}}$\n*   ${\\frac{1}{2}, \\frac{1}{2}, \\frac{1}{2}, \\frac{1}{2}}$"],["2525 425","687232272"]],"created_at":"2026-03-03 11:01:13"}}