You are given a string $s$, consisting of $n$ lowercase English letters.

Rudeness of a string $t$ of length $k$ is the number of pairs of integers $(i,j)$, where $1≤i<j≤k$, for which $t_i=$«a» and $t_j=$«b». In other words, the rudeness of a string is the number of ways to delete all but two of its characters, so that the string «ab» remains.

Your task is to find a substring $s_ls_{l+1}…s_r$, the rudeness of which does not exceed $c$, of maximum length.

The first line of the input contains two integers $n, c\ (1≤n≤10^6,\ 0≤c≤10^{18})$.

The second line contains the string $s$. The string consists of $n$ lowercase English letters.

Print a single integer, the maximum length of a substring of a string that has rudeness at most $c$.