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 = input()

a = [0]
i = 0
p = "1"
for t in s:
  if t == p:
    a[i] += 1
  else:
    p = t
    i += 1
    a += [1]
a += [0]
# print(a)

if len(a) <= 2*k+1:
  print(sum(a))
  quit()

x = sum(a[:2*k+1])
m = x 
for i in range(2*k+1,len(a)):
  # print(i, a[i] , a[i-(2*k+1)])
  x = x + a[i] - a[i-(2*k+1)]
  if i%2 == 0:
    m = max(m,x)
print(m)