{"raw_statement":[{"iden":"problem statement","content":"You are given a string $S$ of length $N$ consisting of the characters `A`, `B`, and `C`.\nConsider performing the following operation between $0$ and $K$ times, inclusive:\n\n*   Freely choose two characters in $S$ and swap them.\n\nFind the number of strings that $S$ can be after the operations, modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 250000$\n*   $1 \\leq K \\leq 100$\n*   $S$ is a string of length $N$ consisting of the characters `A`, `B`, and `C`.\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $K$\n$S$"},{"iden":"sample input 1","content":"3 1\nABC"},{"iden":"sample output 1","content":"4\n\nThe following four strings can be obtained:\n\n*   $S=$`ABC`: No operation is needed.\n*   $S=$`BAC`: Swap the $1$\\-st and $2$\\-nd characters.\n*   $S=$`CBA`: Swap the $1$\\-st and $3$\\-rd characters.\n*   $S=$`ACB`: Swap the $2$\\-nd and $3$\\-rd characters."},{"iden":"sample input 2","content":"3 2\nABC"},{"iden":"sample output 2","content":"6"},{"iden":"sample input 3","content":"4 5\nAAAA"},{"iden":"sample output 3","content":"1"},{"iden":"sample input 4","content":"30 10\nCACCABAABBABABBCBBCAAACAAACCCA"},{"iden":"sample output 4","content":"42981885"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}