{"raw_statement":[{"iden":"problem statement","content":"Given is a string $S$ consisting of `0` and `1`. Find the number of strings, modulo $998244353$, that can result from applying the following operation on $S$ between $0$ and $K$ times (inclusive):\n\n*   Choose a pair of integers $i, j$ $(1\\leq i < j\\leq |S|)$ such that the $i$\\-th and $j$\\-th characters of $S$ are `0` and `1`, respectively. Remove the $j$\\-th character from $S$ and insert it to the immediate left of the $i$\\-th character."},{"iden":"constraints","content":"*   $1 \\leq |S| \\leq 300$\n*   $0 \\leq K \\leq 10^9$\n*   $S$ consists of `0` and `1`."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$S$ $K$"},{"iden":"sample input 1","content":"0101 1"},{"iden":"sample output 1","content":"4\n\nFour strings, `0101`, `0110`, `1001`, and `1010`, can result."},{"iden":"sample input 2","content":"01100110 2"},{"iden":"sample output 2","content":"14"},{"iden":"sample input 3","content":"1101010010101101110111100011011111011000111101110101010010101010101 20"},{"iden":"sample output 3","content":"113434815"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}