{"problem":{"name":"Stop. Otherwise...","description":{"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 $998244353$: * ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc102_c"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $1 \\leq K \\leq 2000$\n*   $2 \\leq N \\leq 2000$\n*   $K$ and $N$ are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$K$ $N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc102_c","tags":[],"sample_group":[["3 3","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 $4$."],["4 5","36\n36\n20\n20\n20\n36\n36"],["6 1000","149393349\n149393349\n668669001\n668669001\n4000002\n4000002\n4000002\n668669001\n668669001\n149393349\n149393349"]],"created_at":"2026-03-03 11:01:14"}}