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)

def solve():
  N, K = map(int, input().split())
  s = input()
  print(s)
  S = []
  look = s[0]
  cnt = 0
 
  if s[0] == '0': S.append(0)
  for c in s:
    if look == c: cnt += 1
    else:
      S.append(cnt)
      cnt = 1
      look = c
  S.append(cnt)
  if s[-1] == '0': S.append(0)
 
  num = min(len(S), 2 * K + 1)
  part = sum(S[0:num])
  ans = part
 
  for i in range(0, len(S) - num, 2):
    part += - sum(S[i:i+2]) + sum(S[i + num:i + num + 2])
    ans = max(ans, part)
  return ans
 
print(solve())