{"problem":{"name":"Dice Sum","description":{"content":"How many integer sequences of length $N$, $A=(A_1, \\ldots, A_N)$, satisfy all of the conditions below? *   $1\\le A_i \\le M$ $(1 \\le i \\le N)$      *   $\\displaystyle\\sum _{i=1}^N A_i \\leq K$      Si","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc248_c"},"statements":[{"statement_type":"Markdown","content":"How many integer sequences of length $N$, $A=(A_1, \\ldots, A_N)$, satisfy all of the conditions below?\n\n*   $1\\le A_i \\le M$ $(1 \\le i \\le N)$\n    \n*   $\\displaystyle\\sum _{i=1}^N A_i \\leq K$\n    \n\nSince the count can get enormous, find it modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq N, M \\leq 50$\n*   $N \\leq K \\leq NM$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc248_c","tags":[],"sample_group":[["2 3 4","6\n\nThe following six sequences satisfy the conditions.\n\n*   $(1,1)$\n*   $(1,2)$\n*   $(1,3)$\n*   $(2,1)$\n*   $(2,2)$\n*   $(3,1)$"],["31 41 592","798416518\n\nBe sure to print the count modulo $998244353$."]],"created_at":"2026-03-03 11:01:13"}}