{"raw_statement":[{"iden":"problem statement","content":"The AtCoder language has $L$ different characters. How many $N$\\-character strings $s$ consisting of characters in the AtCoder language satisfy the following condition? Find the count modulo $998244353$.\n\n*   All $K$\\-character subsequences of the string $s$ are different. More precisely, there are $_N\\mathrm{C}_K$ ways to obtain a $K$\\-character string by extracting $K$ characters from the string $s$ and concatenating them without changing the order, and all of these ways must generate different strings.\n\nWhat is $_N\\mathrm{C}_K$?$_N\\mathrm{C}_K$ refers to the total number of ways to choose $K$ from $N$ items. More precisely, $_N\\mathrm{C}_K$ is the value of $N!$ divided by $K! \\times (N-K)!$."},{"iden":"constraints","content":"*   $1 \\leq K < N \\leq 500000$\n*   $1 \\leq L \\leq 10^9$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $K$ $L$"},{"iden":"sample input 1","content":"4 3 2"},{"iden":"sample output 1","content":"2\n\nIf `a` and `b` represent the first and second characters in the language, the condition is satisfied by two strings: `abab` and `baba`."},{"iden":"sample input 2","content":"100 80 26"},{"iden":"sample output 2","content":"496798269\n\nApproximately $10^{86}$ strings satisfy the condition, but here we print the count modulo $998244353$, which is $496798269$."},{"iden":"sample input 3","content":"100 1 26"},{"iden":"sample output 3","content":"0"},{"iden":"sample input 4","content":"500000 172172 503746693"},{"iden":"sample output 4","content":"869120"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}