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 Python (3.4.3) (judge verdict: Accepted)

import sys
input = sys.stdin.readline

import copy

def main(): 

    N, K = map(int,input().split())
    S=input().split()
    S=list(S[0])

    list_01 = []
    now=1
    count=0
    for i in range(N):
        if int(S[i]) != now:
            list_01.append(count)
            now=1-now
            count=1
        else:
            count+=1
    if count != 0: list_01.append(count)
    if len(list_01)%2==0: list_01.append(0)
    
    Add = 2*K+1
    left = 0
    right = 0
    ans=0
    i=0
    tmp = 0
    while i < len(list_01):
        nextleft = i
        nextright = min(i+Add,len(list_01))

        while left < nextleft:
            tmp-=list_01[left]
            left+=1
        while right < nextright:
            tmp+=list_01[right]
            right+=1
        ans=max(tmp,ans)
        i+=2
    print(ans)
if __name__ == "__main__":
    main()