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 int_raw():
    return int(input())


def ss_raw():
    return raw_input().split()


def ints_raw():
    return list(map(int, ss_raw()))


N, K = ints_raw()
S = [int(s) for s in raw_input()]
current = S[0]
count = 0
stand_array = []
reverse_array = []
if current == 0:
    reverse_array.append(0)
for s in S:
    if s == current:
        count += 1
    else:
        if current == 1:
            reverse_array.append(count)
        else:
            stand_array.append(count)
        count = 1
        current = 1 - current
if current == 1:
    reverse_array.append(count)
else:
    stand_array.append(count)
if current == 0:
    reverse_array.append(0)

if len(stand_array) <= K:
    print(N)
else:
    max_score = 0
    score = 0
    for i in range(K):
        score += stand_array[i]
        score += reverse_array[i]
    score += reverse_array[K]
    max_score = score
    for i in range(len(stand_array) - K):
        score -= stand_array[i]
        score -= reverse_array[i]
        score += stand_array[i + K]
        score += reverse_array[i + K + 1]
        max_score = max(score, max_score)
    print(max_score)
