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 \(c\).