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<iostream>
#include<string>
using namespace std;
#define N 100005

int n,k,ans;
string s;
int l[N],r[N];
int cnt;

int main()
{
	
	cin>>n>>k;
	cin>>s;
	for(int i=0;i<s.size();i++)
		if(s[i]=='0')
		{
			cnt++;
			l[cnt]=i;
			while(s[i]=='0') i++;
			i--;
			r[cnt]=i;
		}
	r[0]=-1;
	l[cnt+1]=n;
	if(k>cnt) k=cnt;
	
	for(int i=k;i<=cnt;i++)
		ans=max(ans,l[i+1]-r[i-k]-1);
	cout<<ans<<'\n';
	
	return 0;
}