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() {
	int N, K, ans = 0, R = 1, count;
	string S;
	cin >> N >> K >> S;
	count = (S[0] == '0');
	for (int L = 0; L < N; L++) {
		if (L != 0 && S[L] == '1' && S[L - 1] == '0') count--;
		while (R < N) {
			if (S[R] == S[R - 1] || S[R] == '1') R++;
			else if (count < K) count++, R++;
			else break;
		}
		ans = max(ans, R - L);
	}
	cout << ans;
}