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
from itertools import accumulate

N, K = map(int, input().split())
S = input() + "2"
T = []
i = 0
for j in range(1, len(S)):
    if S[i] != S[j]:
        T.append(j - i)
        i = j
U = [0] + list(accumulate(T))
ans = 0
for i in range(len(T)):
    if (i + int(S[0])) % 2 == 0:
        j = i + 2 * (K - 1) + 1
    else:
        j = i + 2 * K
    j = min(j, len(T) - 1)
    ans = max(ans, U[j + 1] - U[i])
print(ans)
