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 N,K,ans = 1;
string S;
 
int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
 
	cin >> N >> K >> S;
 
	int cnt=0,len=0;
 
	for(int i=0;i<N;++i){
		if(S[i] =='0'){
			if(i == 0 || S[i - 1] == '1'){
				cnt++;
			}
		}
		if(cnt > K){
			while(S[len] == '1'){
				len++;
			}
			while(S[len] == '0'){
				len++;
			}
			cnt--;
		}
		ans = max(ans,i - len + 1);
	}
 
 
	cout << ans << endl;
}