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 = [ int(it) for it in input().split() ]
S = [ int(it) for it in input() ]

li = []

v = 1
c = 0
for it in S:
  if (v != it ):
    li.append(c)
    c=1
  else:
    c+=1
  v = it
li.append(c)
s = 0
lis = [0]*(len(li)+1)
for i in range(len(li)):
  lis[i+1]=lis[i]+li[i]
s = 0
for i in range(N):
  if (i*2>=N):
    continue
  a = min(i*2,len(li))
  b = min(i*2+2*K+1,len(li))

  ds2 = lis[b]-lis[a]
  s = max(s,ds2)
print (s)
