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=[int(i) for i in input()]
l1,l0=[],[]
b,c=1,0
for i in s:
  if b==i: c+=1
  else:
    if b: l1+=[c]
    else: l0+=[c]
    c=1
  b=i
if b:
  l1+=[c]
  l0+=[0]
else:
  l0+=[c]
S=[0]
for i,j in zip(l1,l0):
  S+=[S[-1]+i+j]
l1+=[0]
m=len(S)
if m<=k:
  print(n)
  exit()
a=0
for i in range(k,m):
  a=max(a,S[i]-S[i-k]+l1[i])
print(a)