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())
w=input()
l=[]
c=0
w="1"+w
for i in range(1,1+n):
  if w[i]!=w[i-1]:
    l.append(c)
    c=1
  else:
    c+=1
l.append(c)
if k>=len(l)//2:
  print(n)
else:
  if w[-1]=="0":
    l.append(0)
  s=l[0]
  for i in range(1,1+k):
    s+=l[2*i]+l[2*i-1]
  s1=s
  c1=l[0]+l[1]
  for i in range(1,(len(l)+1)//2-k):
    s1=s1-l[2*i-2]-l[2*i-1]+l[2*i-1+2*k]+l[2*i+2*k]
    if s1>s:
      s=s1
  print(s)