{"raw_statement":[{"iden":"problem statement","content":"How many integer sequences $A=(A_1,\\ldots,A_N)$ of length $N$ satisfy all the conditions below?\n\n*   $1\\le A_i \\le M$ $(1 \\le i \\le N)$\n    \n*   $|A_i - A_{i+1}| \\geq K$ $(1 \\le i \\le N - 1)$\n    \n\nSince the count can be enormous, find it modulo $998244353$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 1000$\n*   $1 \\leq M \\leq 5000$\n*   $0 \\leq K \\leq M-1$\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 1"},{"iden":"sample output 1","content":"6\n\nThe following $6$ sequences satisfy the conditions.\n\n*   $(1,2)$\n*   $(1,3)$\n*   $(2,1)$\n*   $(2,3)$\n*   $(3,1)$\n*   $(3,2)$"},{"iden":"sample input 2","content":"3 3 2"},{"iden":"sample output 2","content":"2\n\nThe following $2$ sequences satisfy the conditions.\n\n*   $(1,3,1)$\n*   $(3,1,3)$"},{"iden":"sample input 3","content":"100 1000 500"},{"iden":"sample output 3","content":"657064711\n\nPrint the count modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}