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 = input()

index_lst = []
num_lst = []
before = '-1'
for K, i in enumerate(s):
    if i != before:
        before = i
        index_lst.append(K)
        num_lst.append(int(i))
N = len(index_lst)
index_lst += [n] * (2*k+10)

S = 0
for i in range(N):
    S = max(S, index_lst[i+2*k] - index_lst[i]) if num_lst[i] == 0 else max(S, index_lst[i+2*k+1] - index_lst[i])
print(S)