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]
X = ['1']
pos = 0
for i in range(N):
  if S[i] != X[pos]:
    L.append(1)
    X.append(S[i])
    pos += 1
  else:
    L[pos] += 1
while pos < 2 * K + 4:
  L.append(0)
  X.append('1')
  pos += 1
L.append(0)
X.append('1')
n = len(L)
for i in range(1, n):
  L[i] += L[i-1]
M = L[2*K]
for i in range(1, n-2*K):
  if X[i] == '1':
    M = max(L[2*K+i] - L[i-1], M)
print(M)