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():
    N, K = [int(_) for _ in raw_input().split()]
    S = raw_input()
    elms = [S[0]]
    cnts = []
    cnt = 1
    for i in range(1,N):
        if S[i] == elms[-1]:
            cnt += 1
        else:
            cnts.append(cnt)
            elms.append(S[i])
            cnt = 1
    cnts.append(cnt)
    num_elm = len(elms)
    max_cont1 = 0
    tmp = 0
    for i in range(num_elm):
        if i == 0:
            if elms[i] == '0':
                tmp = sum(cnts[i:(i+2*K)])
                max_cont1 = max(max_cont1, tmp)
            if elms[i] == '1':
                tmp = sum(cnts[i:(i+2*K+1)])
                max_cont1 = max(max_cont1, tmp)
        elif i == 1:
            if elms[i] == '1':
                tmp -= cnts[i-1]
                if i + 2*K - 1 < num_elm:
                    tmp += cnts[i + 2*K - 1]
                if i + 2*K < num_elm:
                    tmp += cnts[i + 2*K]
                max_cont1 = max(max_cont1, tmp)
        else:
            if elms[i] == '1':
                tmp -= cnts[i - 2]
                tmp -= cnts[i - 1]
                if i + 2*K - 1 < num_elm:
                    tmp += cnts[i + 2*K - 1]
                if i + 2*K < num_elm:
                    tmp += cnts[i + 2*K]
                max_cont1 = max(max_cont1, tmp)
    print str(max_cont1)

if __name__ == '__main__':
    solve()
