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, raw_input().split())
S=raw_input()

if "0" not in S:
	print len(S)
	quit()
L=[]
if S[0]=="0": L.append(0)
for i,x in enumerate(S):
	if i==0:
		cnt=1
	else:
		if prev==x:
			cnt+=1
		else:
			L.append(cnt)
			cnt=1
	prev=x
else:
	L.append(cnt)

if S[-1]=="0": L.append(0)

LSUM=[0]
for x in L:
	LSUM.append(LSUM[-1]+x)

K=min(K,len(L)/2)

ans=0
len_lsum=len(LSUM)
for l in range(0,len_lsum,2):
	r=l+2*K+1
	if r < len_lsum:
		ans=max(ans , LSUM[r]-LSUM[l])

print ans

