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 = [0]
curr = '1'
for c in S:
    if c != curr:
        l.append(1)
        curr = c
    else:
        l[-1] += 1
if curr == '0':
    l.append(0)

n_group = len(l) // 2
sum_ = 0
k = min(K, n_group)
sum_ = sum(l[0:2*k+1])
max_ = sum_
for i in range(k, n_group):
    sum_ -= l[2*i-2*K] + l[2*i+1-2*K]
    sum_ += l[2*i+1] + l[2*i+2]
    max_ = max(max_, sum_)
print(max_)