Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 1
00010

Sample Output 1

4

We can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:

Give the direction with l = 1, r = 3, which flips the first, second and third persons from the left.

Sample Input 2

14 2
11101010110011

Sample Output 2

8

Sample Input 3

1 1
1

Sample Output 3

1

No directions are necessary.

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

n,k=map(int,input().split())
s=list(str(input()))
r=[]
l=[]
c=0
d=1
for i in range(n):
	if s[i]=='1' and d==1:
		r.append(i)
		c=1
		d=0
	elif s[i]=='0' and c==1:
		l.append(i-1)
		c=0
		d=1
if c>0:
	l.append(i)
if len(r)<=k+1:
	r=[0]*(k+1-len(r))+r+[n-1]*(k+1-len(r))
	l=[0]*(k+1-len(l))+l+[n-1]*(k+1-len(l))
ans=0
for i in range(k+1):
	ans=max(ans,l[i+k]-r[i]+1)
print(ans)