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)

input_array = [int(i) for i in input().split()]
S = str(input())

N = int(input_array[0])
K = int(input_array[1])

S_array = list(S)

S_count_array = [0]

count = 0
for i in range(len(S_array)):
  if i == 0:
    S_count_array[count] = 1
  else:
    if S_array[i] == S_array[i-1]:
      S_count_array[count] += 1
    else:
      S_count_array.append(1)
      count += 1

sum_s_number = []
if S_array[0] == "0":
  for i in range(len(S_count_array)):
    if (i+1) % 2 == 0:
      sum_s_number.append(sum(S_count_array[i:i+(K*2)+1]))
    else:
      sum_s_number.append(sum(S_count_array[i:i+(K*2)]))

else:
  for i in range(len(S_count_array)):
    if (i+1) % 2 == 0:
      sum_s_number.append(sum(S_count_array[i:i+(K*2)]))
    else:
      sum_s_number.append(sum(S_count_array[i:i+(K*2)+1]))

print(max(sum_s_number))