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=100050;
int n,k,cnt,ans,p=1;
string s;
vector<int> vec;

int main()
{
cin>>n>>k>>s;
cnt=(s[0]=='0');
  for (int i=0; i<n; i++)
  {
	if(i && s[i]=='1' && s[i-1]=='0')
	  cnt--;
	while(p<n)
	{
	  if(s[p-1]==s[p])
		p++;
	  else if(s[p]=='1')
		p++;
	  else if(cnt<k)
		cnt++,p++;
	  else
		break;
	}
	ans=max(ans,p-i);
  }
cout<<ans<<endl;
}
