{"raw_statement":[{"iden":"problem statement","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 $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N, M \\leq 50$\n*   $N \\leq K \\leq NM$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$ $K$"},{"iden":"sample input 1","content":"2 3 4"},{"iden":"sample output 1","content":"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*   $(3,1)$"},{"iden":"sample input 2","content":"31 41 592"},{"iden":"sample output 2","content":"798416518\n\nBe sure to print the count modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}