N people are arranged in a row from left to right.

You are given a string S of length N consisting of `0` and `1`, and a positive integer K.

The 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`.

You will give the following direction at most K times (possibly zero):

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.

Find the maximum possible number of consecutive people standing on hands after at most K directions.

Constraints

* N is an integer satisfying 1 \leq N \leq 10^5.
* K is an integer satisfying 1 \leq K \leq 10^5.
* The length of the string S is N.
* Each character of the string S is `0` or `1`.

Input

Input is given from Standard Input in the following format:


N K
S


Output

Print the maximum possible number of consecutive people standing on hands after at most K directions.

Examples

Input

5 1
00010


Output

4


Input

14 2
11101010110011


Output

8


Input

1 1
1


Output

1
#include <bits/stdc++.h>
using namespace std;
//D - Handstand
int a[100001];
int main(void){
    int n,k,m=0;
    string s;
    std::cin >> n >> k >>s;
    
    s += '1';
    for (int i = 0; i < n; i++) {
        a[i+1]=a[i];
        if(s[i]=='0' && s[i+1] =='1')
            a[i+1]++;
    }
    for(int l=0,r=1;r<=n;){
        if(a[r]-a[l]>k)l++;
        else{
            if(r==n || s[r-1]=='1')
                m=max(m,r-l);
            r++;
        }
    }
    std::cout << m << std::endl;
    return 0;
}