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: Accepted)

def main():
  import sys
  input = sys.stdin.readline
  import numpy as np
  n,k = map(int,input().split())
  s = input()
  chk_0 = []
  chk_1 = []
  c0 = 0
  c1 = 0
  if s[0]=='0':
    c0 += 1
  else:
    c1 += 1
    chk_0.append(0)

  for i in range(n-1):
    if s[i]=='0' and s[i+1]=='0':
      c0 += 1
    if s[i]=='0' and s[i+1]=='1':
      chk_0.append(c0)
      c0 = 0
      c1 = 1
    if s[i]=='1' and s[i+1]=='0':
      chk_1.append(c1)
      c0 = 1
      c1 = 0
    if s[i]=='1' and s[i+1]=='1':
      c1 += 1

  if c0 != 0:
    chk_0.append(c0)
    chk_1.append(0)
  elif c1 != 0:
    chk_1.append(c1)
    chk_0.append(0)

  if len(chk_0) <= k:
    print(n)
    exit()

  ab = np.array([x+y for x,y in zip(chk_0,chk_1)])
  np.cumsum(ab,out=ab)

  ans = ab[k-1]
  for i in range(len(ab)-k):
    chk = ab[k+i]-ab[i]
    chk += chk_1[i]
    ans = max(ans,chk)
  print(ans)
if __name__ == '__main__':
    main()