{"problem":{"name":"Ball","description":{"content":"You are given integers $N, M, K$.   For each $m = 1, 2, \\dots, M$, solve the following problem: > There are $N$ balls numbered $1$ through $N$, and $m+1$ boxes numbered $0$ through $m$.   > Box $0$ c","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"fps_24_p"},"statements":[{"statement_type":"Markdown","content":"You are given integers $N, M, K$.  \nFor each $m = 1, 2, \\dots, M$, solve the following problem:\n\n> There are $N$ balls numbered $1$ through $N$, and $m+1$ boxes numbered $0$ through $m$.  \n> Box $0$ can hold at most $K$ balls. The other boxes have no upper limit.  \n> Find the number of ways to place all $N$ balls into the boxes, modulo $998244353$.  \n> Two placements are considered different if there exists at least one ball that is placed in different boxes between the two placements.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq M \\leq 10^5$\n*   $1 \\leq K \\leq N$\n*   All input values are integers\n\n## Input\n\nThe input is given from standard input in the following format:\n\n$N$ $M$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"fps_24_p","tags":[],"sample_group":[["3 2 1","4\n20\n\nConsider the case $m=1$. There are $4$ valid placements of the balls:\n\n*   Put balls $1,2,3$ into box $1$.\n*   Put ball $1$ into box $0$, and balls $2,3$ into box $1$.\n*   Put ball $2$ into box $0$, and balls $1,3$ into box $1$.\n*   Put ball $3$ into box $0$, and balls $1,2$ into box $1$."],["12345 5 6789","583034791\n982161077\n613932842\n770852810\n194914198"]],"created_at":"2026-03-03 11:01:14"}}