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, raw_input().split())
S = raw_input()

T = []
if S[0]=="0":
  T = [0]
p = 0
for i in range(1, N+1):
  if i==N or S[i]!=S[i-1]:
    T += [i-p]
    p = i
if S[-1]=="0":
  T += [0]

if len(S)<=2*K+1:
  ans = sum(T)
else:
  t = sum(T[:2*K+1])
  ans = t
  for i in range(2*K+1, len(T)):
    t -= T[i-2*K-1]
    t += T[i]
    if i%2==0:
      ans = max(ans, t)
print ans
