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: Runtime Error)

import numpy as np
s=input().split()
k=int(s[1])
ini=list(input())
n=len(ini)

a1 = np.array([])
b = 0
c = 0
for i in range(n):
    if ini[i] == "0":
        if b > 0:
            a1=np.append(a1,b)
            b = 0
        c = c+1
    if ini[i] == "1":
        if c > 0:
            a1=np.append(a1, c)
            c = 0
        b = b+1
    if i == n-1:
        if b > 0:
            a1=np.append(a1,b)
            b = 0
        if c > 0:
            a1=np.append(a1, c)
            c = 0
            
elem=2*k+1
m=np.size(a1)
cands=np.array([])

if ini[0] == "1":
    for i in range((m-elem+1)//2+2):
        cand = np.sum(a1[2*i:2*i+elem])
        cands=np.append(cands,cand)
if ini[0] == "0":
    for i in range((m-elem+1)//2+2):
        cand = np.sum(a1[2*i+1:2*i+1+elem])
        cands=np.append(cands,cand)
        
print(int(np.max(cands)))