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
# solution

nim,mike=map(int,input().split())
data=input()
X=[]
Y=[0]
_s='2'
for i,s in enumerate(data):
  if _s!=s:
    _s=s
    X.append(i)
    Y.append((int(s)+1)%2)
import itertools
Y=list(itertools.accumulate(Y))
ans=[]
for i,x in enumerate(X):
  if Y[-1]-Y[i]<=mike:
    ans.append(nim-x)
    break
  else:
    if data[x]=='0':
      ans.append(X[i+2*mike]-x)
    else:
      ans.append(X[i+2*mike+1]-x)
print(max(ans))