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 = []
c = 1
for i in range(n-1):
    if s[i]==s[i+1]:
        c+=1
    else:
        a.append(c)
        c = 1
a.append(c)
b = [0]
for i in range(len(a)):
    b.append(b[-1]+a[i])
b.append(b[-1])
n = len(b)
l = 2*k+1
st=int(s[0])
ans = 0
for i in range(st,n,2):
    ans = max(ans,b[i]-b[max(0,i-l)])
print(ans)
