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 = []
c = 1
for i in range(n - 1):
    if s[i] != s[i + 1]:
        l.append(c)
        c = 0
    c += 1
l.append(c)
l += [0]
if s[0] == '0':
    l = [0] + l
tmp = sum(l[:2 * k + 1])
rslt = tmp
for i in range(0, len(l) - 2*k-2, 2):
    tmp = tmp - l[i] - l[i + 1] + l[i + 2 * k + 1] + l[i + 2 * k + 2]
    rslt = max(tmp, rslt)
print(rslt)
    