{"raw_statement":[{"iden":"problem statement","content":"Takahashi throws $N$ dice, each having $K$ sides with all integers from $1$ to $K$. The dice are NOT pairwise distinguishable. For each $i=2,3,...,2K$, find the following value modulo $998244353$:\n\n*   The number of combinations of $N$ sides shown by the dice such that the sum of no two different sides is $i$.\n\nNote that the dice are NOT distinguishable, that is, two combinations are considered different when there exists an integer $k$ such that the number of dice showing $k$ is different in those two."},{"iden":"constraints","content":"*   $1 \\leq K \\leq 2000$\n*   $2 \\leq N \\leq 2000$\n*   $K$ and $N$ are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$K$ $N$"},{"iden":"sample input 1","content":"3 3"},{"iden":"sample output 1","content":"7\n7\n4\n7\n7\n\n*   For $i=2$, the combinations $(1,2,2),(1,2,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $7$.\n*   For $i=3$, the combinations $(1,1,1),(1,1,3),(1,3,3),(2,2,2),(2,2,3),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $7$.\n*   For $i=4$, the combinations $(1,1,1),(1,1,2),(2,3,3),(3,3,3)$ satisfy the condition, so the answer is $4$."},{"iden":"sample input 2","content":"4 5"},{"iden":"sample output 2","content":"36\n36\n20\n20\n20\n36\n36"},{"iden":"sample input 3","content":"6 1000"},{"iden":"sample output 3","content":"149393349\n149393349\n668669001\n668669001\n4000002\n4000002\n4000002\n668669001\n668669001\n149393349\n149393349"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}