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
def solve(string):
    n, k, s = string.split()
    n, k = map(int, [n, k])
    flip = [0] + [i for i, (s0, s1) in enumerate(zip(s, s[1:]), start=1) if s0 != s1] + [n]
    start = int(s[0])
    l = len(flip) - 1
    return str(max([flip[min(l, i + 2 * k + (i % 2 ^ start))] - flip[i] for i in range(l + 1)]))


if __name__ == '__main__':
    print(solve('\n'.join([input(), input()])))
