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()

L = S.replace('01', '0,1')
L = L.replace('10', '1,0')
L = L.split(',')
L = [len(l) for l in L]

if S[0] == '0':
    L = [0] + L

R = []
for i in range(max(1, len(L) // 2 + 1 - K)):
    if i == 0:
        R.append(sum(L[2*i:2*(i+K)+1]))
    else:
        R.append(R[-1] - sum(L[2*(i-1):2*(i-1)+2]) + sum(L[2*(i+K)-1:2*(i+K)+1]))

print(max(R))
