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>
using namespace std;

int main() {
	int N, K;
	string S;
	cin >> N >> K >> S;
	int ans = 1;
	for (int l = 0, r = 1, operate = S[0] == '0' ? 1 : 0;r < N;++ r) {
		if (r < N && S[r - 1] == '1' && S[r] == '0') { // rを追加したら操作回数が増えた時
			++ operate;
			if (operate > K) { // 反転回数がオーバーした
				++ l;
				while (S[l - 1] != '0' || S[l] != '1') ++ l;
				-- operate;
			}
		}
		ans = max(ans, r - l + 1);
	}
	cout << ans;
	return 0;
}