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: Time Limit Exceeded)

import sys
from bisect import bisect_left,bisect_right,insort
#input = sys.stdin.readline

def main():
    n,k=map(int,input().split())
    s=list(input())
    flg,cnt,chk='1',0,[0]    
    for i in range(n):
        if s[i]==flg:
            chk[cnt]+=1
        else:
            flg=str((int(flg)+1)%2)
            cnt+=1
            chk.append(1)
    lng=len(chk)
    if k*2>lng:
        print(n)
    else:
        i=1
        ans=0
        while i+2*(k-1)<=n-1:
            ans=max(ans,sum(chk[i-1:i+2*k]))
            i+=2
        print(ans)

if __name__ == '__main__':
    main()