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)

import sys
N, K = map(int, input().split())
S = input()

o = []
z = []

i = 0
while True:
  cnt = 0
  while i <= N-1 and int(S[i]) == 1:
    cnt += 1
    i += 1
  o.append(cnt)
  if i > N-1:
    break
  cnt = 0
  while i <= N-1 and int(S[i]) == 0:
    cnt += 1
    i += 1
  z.append(cnt)
#print(o)
#print(z)

if len(z) <= K:
  print(len(S))
  sys.exit()

num = o[0]
for j in range(K):
  num += z[j]+o[j+1]

max_num = num
for j in range(K, len(z)):
  num -= o[j-K]+z[j-K]
  num += z[j]+o[j+1]
  max_num = max(max_num, num)

print(max_num)