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;

typedef long long ll;
typedef unsigned long long ull;

int main()
{
    ll N, K;
    cin >> N >> K;
    string S;
    cin >> S;
    ll res=0;
    queue<ll> q;
    q.push(0);
    for(ll i=0;i<N;i++){
        while(i<N && S[i]=='0') i++;
        if(i>0) q.push(i);
        while(i<N && S[i]=='1') i++;
        if(q.size()>K){
            auto istart = q.front(); q.pop();
            res = max(res, i-istart);
        }
    }
    if(res==0){
        cout<<N<<endl;
    }else{
        cout<<res<<endl;
    }

    return 0;
}