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;

int main(){
	ll n,k;
	string s;
	cin>>n>>k;
	cin>>s;
	ll z[n+1],j=0,res=0,sum=0;
	memset(z,0,sizeof(z));
	ll a=0,cnt=k;
	ll right=0,left=0;
	while(right<n){
		while(right<n&&s[right]=='1')right++;
		res = max(res,right-left);
		while(right<n&&s[right]=='0')right++;
		k--;
		if(k<0){
			while(left<n&&s[left]=='1')left++;
			while(left<n&&s[left]=='0')left++;
		}
		res=max(res,right-left);
	}

	cout<<res<<endl;
}
