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: Time Limit Exceeded)

N, K = map(int,input().split())
state_list = [int(_) for _ in input()]
state_num_list = []

counter = 1
prev_num = state_list[0]
# リストの改変
for n in range(1, N):

    if state_list[n] == prev_num:
        counter += 1
        continue
    else:
        state_num_list.append(counter)
        counter = 1
        prev_num = state_list[n]
state_num_list.append(counter)

max_sum = 0
# メイン
start_num = state_list[0]
for s in range(len(state_num_list)):
    count_num = 0
    if start_num == 0:
        count_num = K * 2
    else:
        count_num = K * 2 + 1
    
    check_sum = sum(state_num_list[s:s + count_num])

    max_sum = check_sum if max_sum < check_sum else max_sum
    start_num = 0 if start_num == 1 else 1

print(max_sum)