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)

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

before = S[0]
cnt = 0
same_nums = []
if S[0] == '0':
  same_nums.append(0)
for i in range(N):
  if S[i] == before:
    cnt += 1
  else:
    same_nums.append(cnt)
    before = S[i]
    cnt = 1
same_nums.append(cnt)
if S[-1] == '0':
  same_nums.append(0)
  
sum_nums = sum(same_nums[:2*K+1])
ans = sum_nums
for i in range(0, len(same_nums)-2*K, 2):
  sum_nums = sum_nums - sum(same_nums[i:i+2]) + sum(same_nums[i+2*K+1:i+2*K+3])
  ans = max(ans, sum_nums)
print(ans)