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=[]
a.append(0)
for i in range(len(s)-1):
	if s[i] != s[i+1]:
		a.append(i+1)
a.append(n)
if s[-1]=='0':
	m=2*k
else:
	m=2*k+1
t=4*k+1
_max=0
i=len(a)-1
if i- m<0:
	print(n)
else:
	while i-m>=0:
		tmp=a[i]-a[i-m]
		#print('i:{} tmp:{}'.format(i,tmp))
		if tmp>_max:
			_max=tmp
		m=t-m
		i-=1
	if a[i]>_max:
		_max=a[i]
	print(_max)