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 main() {
	string s;
	int n, k;
	cin >> n >> k >> s;
	s += '0';
	int ans = 0,co=0,gg=0;
	if (n == 1) {
		cout << 1 << endl;
		return 0;
	}
	if (s[0] == '0')
		co++;
	for (int i = 0;i < n;i++) {
		if (s[i] == '1' && s[i+1] == '0') {
			if (co == k) {
				ans = max(ans, i -gg+1);
				gg++;
				while (s[gg-1] != '0' || s[gg] != '1')
					gg++;
			}
			else
				co++;
		}
	}
	ans = max(ans, n - gg);
	cout << ans << endl;
}
