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()

change = [0]
for i, (e1, e2) in enumerate(zip(s, s[1:])):
	e1 = int(e1)
	e2 = int(e2)
	if e1 ^ e2:
		change.append(i + 1)

change.append(n)
end = len(change) - 1

ans = 0
for i, l in enumerate(change[:-1]):
	if s[l] == "1":
		ri = min(i + 2 * k + 1, end)
	else:
		ri = min(i + 2 * k, end)

	r = change[ri]

	ans = max(ans, r - l)

print(ans)
