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()
A = []
if S[0] == '0':
  A.append(0)
i = 0
while i < len(S):
  j = i
  while j < len(S) and S[i] == S[j]:
    j += 1
  A.append(j - i)
  i = j
ans = 0
tot = 0
r = 0
for l in range(len(A)):
  while r < len(A) and r - l < 2 * K + 1:
    tot += A[r]
    r += 1
  if l % 2 == 0:
    ans = max(ans, tot)
  if r == l:
    r += 1
  else:
    tot -= A[l]
print(ans)
