You are given a string that contains only three characters \(a\), \(b\), and \(c\). You can change at the most \(k\) characters in the string. The uniformity index of a string is defined by the maximum length of the substring that contains the same character. Your task is to determine the maximum uniformity index than can be achieved.

Input format

First line: Two integers \(n\) and \(k\) where \(n\) denotes the size of the string and \(k\) as specified in the question
Second line: A string of length \(n\)

Output format
Print a single integer denoting the maximum uniformity that can be achieved.

Constraints
\(1 \le N \le 10^6\\ 0 \le K \le N\)
The string \(s\) contains only characters \(a\), \(b\), and \(c\).