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)

from operator import add
from collections import deque
from itertools import accumulate

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

if N == 1:
  if S == "1" or K >= 1:
    print(1)
  else:
    print(0)
    
else:
  num = []
  cnt = 1
  ans = 0
  M = 2 * K + 1

  for i in range(1,N):
    if S[i] == S[i - 1]:
      cnt += 1
    else:
      num.append(cnt)
      cnt = 1
  num.append(cnt)

  if S[0] == "0":
    num = [0] + num
  
  acc = list(accumulate(num,add))
  acc = [0] + acc
  A = len(acc)
  
  for left in range(0,A,2):
    right = min(A - 1,left + M)
    ans = max((acc[right] - acc[left]),ans)
    
  print(ans)