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 itertools

n,k = map(int, input().split())
s_str = input()
s = []
for i in s_str:
    s.append(int(i))

s_encoded = []
now = 0
tmp = 0
for i in range(len(s)):
    if i == 0:
        if s[0] == 1:
            s_encoded.append(0)
            now = 1
        else:
            pass
    
    if s[i]==now:
        tmp=tmp+1
    else:
        s_encoded.append(tmp)
        tmp=1
        now = 1 - now
                
    if i==len(s)-1:
        s_encoded.append(tmp)
        
sum_before = []
sum_tmp=0
for i in range(len(s_encoded)):
    sum_tmp = sum_tmp+s_encoded[i]
    sum_before.append(sum_tmp)
max_line=s_encoded[0]
left = 0
if left%2==0:
    right = min(left + 2*(k-1) +1, len(sum_before)-1)
else:
    right = min(left + 2*k, len(sum_before)-1)
right = min(left + 2*(k-1) +1, len(sum_before)-1)
while left < len(sum_before):
    line = sum_before[right] - sum_before[left-1]
    if max_line<line:
        max_line=line
    left = left + 1
    if left%2==0:
        right = min(left + 2*(k-1) +1, len(sum_before)-1)
    else:
        right = min(left + 2*k, len(sum_before)-1)
print(max_line)