{"raw_statement":[{"iden":"problem statement","content":"$N$ people are arranged in a row from left to right.\nYou are given a string $S$ of length $N$ consisting of `0` and `1`, and a positive integer $K$.\nThe $i$\\-th person from the left is standing on feet if the $i$\\-th character of $S$ is `0`, and standing on hands if that character is `1`.\nYou will give the following direction at most $K$ times (possibly zero):\n**Direction**: Choose integers $l$ and $r$ satisfying $1 \\leq l \\leq r \\leq N$, and flip the $l$\\-th, $(l+1)$\\-th, $...$, and $r$\\-th persons. That is, for each $i = l, l+1, ..., r$, the $i$\\-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.\nFind the maximum possible number of **consecutive** people standing on hands after at most $K$ directions."},{"iden":"constraints","content":"*   $N$ is an integer satisfying $1 \\leq N \\leq 10^5$.\n*   $K$ is an integer satisfying $1 \\leq K \\leq 10^5$.\n*   The length of the string $S$ is $N$.\n*   Each character of the string $S$ is `0` or `1`."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$S$"},{"iden":"sample input 1","content":"5 1\n00010"},{"iden":"sample output 1","content":"4\n\nWe can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:\n\n*   Give the direction with $l = 1, r = 3$, which flips the first, second and third persons from the left."},{"iden":"sample input 2","content":"14 2\n11101010110011"},{"iden":"sample output 2","content":"8"},{"iden":"sample input 3","content":"1 1\n1"},{"iden":"sample output 3","content":"1\n\nNo directions are necessary."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}