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
n, k = map(int, input().split())
s = list(input())


L = [0]
R = []
for i, (a, b) in enumerate(zip(s, s[1:])):
    if (a, b) == ('0', '1'):
        L.append(i+1)

    if (a, b) == ('1', '0'):
        R.append(i)
else:
    R.append(n-1)

ans = R[0]-L[0]+1
if s[0] == '0':
    k -= 1
k = min(k, len(R)-1)
for l, r in zip(L, R[k:]):
    x = r-l+1
    if ans < x:
        ans = x
print(ans)
