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)

N,K = map(int,input().split())
S = input()
L = []
cur = S[0]
cnt = 0
if S[len(S)-1] == '1':
  S += '0'
else:
  S += '1'
for i in range(len(S)):
  if S[i] == cur:
    cnt += 1
  else:
    L.append(cnt)
    cnt = 1
    cur = S[i]
ruiseki = [L[0]]
for i in range(len(L)-1):
  ruiseki.append(ruiseki[i]+L[i+1])
ruiseki.insert(0,0)
if len(ruiseki) == 2:
  print(len(S)-1)
else:
  if S[0] == '1' and S[len(S)-2] == '1':
    if (len(L)-1)/2 > K:
      ans = 0
      for i in range(len(ruiseki)-2*K-1):
        if i%2 == 0:
          if ans <= ruiseki[i+2*K+1]-ruiseki[i]:
            ans = ruiseki[i+2*K+1]-ruiseki[i]
      print(ans)
    else:
      print(len(S)-1)
  elif S[0] == '1' and S[len(S)-2] == '0':
    if len(L)/2 > K:
      ans = 0
      for i in range(len(ruiseki)-2*K-2):
        if i%2 == 0:
          if ans <= ruiseki[i+2*K+1]-ruiseki[i]:
            ans = ruiseki[i+2*K+1]-ruiseki[i]
      print(max(ans,ruiseki[len(ruiseki)-1]-ruiseki[len(ruiseki)-1-2*K]))
    else:
      print(len(S)-1)
  elif S[0] == '0' and S[len(S)-2] == '1':
    if len(L)/2 > K:
      ans = 0
      for i in range(len(ruiseki)-2*K):
        if i%2 == 0:
          if ans <= ruiseki[i+2*K]-ruiseki[i]:
            ans = ruiseki[i+2*K]-ruiseki[i]
      print(ans)
    else:
      print(len(S)-1)
  else:
    ans = 0
    if (len(L)+1)/2 > K:
      for i in range(len(ruiseki)-2*K-3):
        if i%2 != 0:
          if ans <= ruiseki[i+2*K+1]-ruiseki[i]:
            ans = ruiseki[i+2*K+1]-ruiseki[i]
      print(max(ans,ruiseki[2*K]-ruiseki[0],ruiseki[len(ruiseki)-1]-ruiseki[len(ruiseki)-1-2*K]))
    else:
      print(len(S)-1)