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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n, k = map(int, input().split())
s = input()
 
if s[0]== "1":
  patterns = []
else:
  patterns = [0]

last = "1"
cnt = 1
 
for i, l in enumerate(s):
  if l == last:
    cnt += 1
    if i == len(s) - 1:
      patterns.append(cnt)
  else: # 変化があったとき
    last = l
    patterns.append(cnt)
    cnt = 1
    
max_len = 1


#print(patterns)
#偶数番目が１の人たち
if len(patterns) <= 2 * k + 1:
  print(len(s))
else:
  for i in range(2*k+1 , len(patterns) + 1, 2):
    length = sum(patterns[i-2*k-1 : i])
    #print(i, length)
    if length >= max_len:
      max_len = length

  print(max_len)