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: Wrong Answer)

import sys
from collections import deque
input = sys.stdin.readline


def main():
    n,k = map(int,input().split())
    s = list(input())
    tank = []
    judge = True
    if s[0] == '0':
        judge = False
    cnt = 0
    for i in range(n):
        if judge:
            if s[i] == '0':
                tank.append(cnt)
                judge = False
                cnt = 0
            cnt += 1
        else:
            if s[i] == '1':
                tank.append(cnt)
                judge = True
                cnt = 0
            cnt += 1
        if i == n-1:
            tank.append(cnt)
    #print(tank)
    p = len(tank)
    if s[0] == '0' and (p+1)//2 <= k:
        print(n)
        exit()
    if p//2 <= k and s[0] == '1':
        print(n)
        exit()

    ans = 0
    res = 0
    if s[0] == '0':
        for j in range(2*k):
            res += tank[j]
        ans = res
        for j in range(2*k,p):
            if j == 2*k:
                res -= tank[0]
            elif j%2 == 0:
                res= res - tank[j-2*k] -tank[j-2*k+1]
            res += tank[j]
            ans = max(ans,res)

    else:
        for j in range(2*k+1):
            res += tank[j]
        ans = res
        for j in range(2*k+1,p):
            if j % 2 == 1:
                res = res- tank[j-2*k-1]-tank[j-2*k]
            res += tank[j]
            ans = max(ans,res)
        exit()
    print(ans)

if __name__ == '__main__':
    main()