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;

int main(){
    int N,K;
    string s;
    scanf("%d%d",&N,&K);
    cin>>s;
    int l=0,r=0;
    queue<int>que;
    int ans=0;
    while(r<N) {
        if(s[r]=='0') {
            while(s[r]=='0') r++;
            r=r-1;
            que.push(r);
        }
        if(que.size()>K) {
            l = que.front(); que.pop();
            l = l+1;
            ans = max(ans,r-l+1);
        }
        ans = max(ans,r-l+1);
//        cout<<ans<<endl;
        r++;
    }
    cout<<ans<<endl;
    return 0;
}
