{"raw_statement":[{"iden":"problem statement","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 $x$."},{"iden":"constraints","content":"*   $1 \\leq M \\leq N \\leq 5000$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"4 2"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"7 7"},{"iden":"sample output 2","content":"1\n3\n4\n3\n2\n1\n1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}