High school student Vasya got a string of length n as a birthday present. This string consists of letters 'a' and 'b' only. Vasya denotes beauty of the string as the maximum length of a substring (consecutive subsequence) consisting of equal letters.

Vasya can change no more than k characters of the original string. What is the maximum beauty of the string he can achieve?

The first line of the input contains two integers n and k (1 ≤ n ≤ 100 000, 0 ≤ k ≤ n) — the length of the string and the maximum number of characters to change.

The second line contains the string, consisting of letters 'a' and 'b' only.

Print the only integer — the maximum beauty of the string Vasya can achieve by changing no more than k characters.

In the first sample, Vasya can obtain both strings "aaaa" and "bbbb".

In the second sample, the optimal answer is obtained with the string "aaaaabaa" or with the string "aabaaaaa".

#include <bits/stdc++.h>

using namespace std;

const int maxn = ;

char str[maxn];

int numb[maxn];

int numa[maxn];

int main()

{

    //freopen("in.txt","r",stdin);

    int n,k;

    scanf("%d%d",&n,&k);

    scanf("%s",str+);

    for(int i = ; i <= n; i++) {

        if(str[i]=='b')

            numb[i] = numb[i-] + ;

        else numb[i] = numb[i-];

        if(str[i]=='a')

            numa[i] = numa[i-] + ;

        else numa[i] = numa[i-];

    }

    int L = ;

    int R = ;

    int ans = ;

    int tmp = ;

    int pos = ;

    while(R<=n) {

        while(R<=n&&numb[R]-tmp<=k) {

            ans = max(ans,R-pos);

            R++;

        }

        pos++;

        tmp=numb[L];

        L++;

    }

    L = ;R = ;

    tmp = ;

    pos = ;

    while(R<=n) {

        while(R<=n&&numa[R]-tmp<=k) {

            ans = max(ans,R-pos);

            R++;

        }

        pos++;

        tmp=numa[L];

        L++;

    }

    printf("%d\n",ans);

    return ;

}