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 numpy as np

b = input().split()
n = int(b[0])
k = int(b[1])
s = input()

arr = []

if int(s[0]) == 0:
    arr.append(0)

before_change = 0
for i in range(1,n):
    if int(s[i - 1]) != int(s[i]):
        arr.append(i - before_change)
        before_change = i
arr.append(n - before_change)
arr = np.array(arr)
#print(arr) 

n_add = 2 * k + 1
ans = 0

if n <= n_add:
    ans = arr.sum()
else:
    i = 0
    while i + n_add <= n:
        temp = arr[i:i+n_add].sum()
        if temp > ans:
            ans = temp
        i += 2

print(ans)