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()
X=[]
j="1"
num=0
for i in S:
    if j!=i:
        X.append(num)
        j=i
        num=1
    else:
        num+=1
X.append(num)

if j=="0":
    X.append(0)
Y=[0]
for i in X:
    Y.append(Y[-1]+i)
ans=0
for i in range(1,len(Y),2):
    t=min(i+2*K,len(Y)-1)
    ans=max(ans,Y[t]-Y[i-1])
print(ans)
