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;
const int N = 2e5 + 10;
int n , k;
string s , t;
int main(){
    cin >> n >> k;
    cin >> s;
    int i = 0 , j = 1 , ans = 1 , cost = 0;
    cost += (s[0] == '0');
    while(j < n){
        if(s[j] == '0' && s[j] != s[j - 1])
            cost++;
        while(cost > k){
            if(s[i] == '0'){
               cost--;
               while(s[i] == '0')i++;
               break;
            }
            i++;
        }
        ans = max(ans , j - i + 1);
        j++;
    }
    cout << ans << endl;
    return 0;
}