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()
st=[0]
for i in range(1,n):
    if(s[i]!=s[i-1]):
        st.append(i)
st.append(n)
a=len(st)-1
if(s[0]=="0"):
    ans=st[min(2*k,a)]
    for i in range(1,a+1,2):
        ans=max(ans,st[min(2*k+1+i,a)]-st[i])
elif(s[0]=="1"):
    ans=0
    for i in range(0,a+1,2):
        ans=max(ans,st[min(2*k+1+i,a)]-st[i])
print(ans)