{"raw_statement":[{"iden":"problem statement","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 $998244353$."},{"iden":"constraints","content":"*   $1 \\leq K \\leq N \\leq 3000$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$"},{"iden":"sample input 1","content":"4 2"},{"iden":"sample output 1","content":"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*   ${\\frac{1}{2}, \\frac{1}{2}, \\frac{1}{2}, \\frac{1}{2}}$"},{"iden":"sample input 2","content":"2525 425"},{"iden":"sample output 2","content":"687232272"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}