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()

s2 = s.replace("01","0,1").replace("10","1,0").split(",")

if s[0]== "1":
  patterns = list(map(len, s2))
else:
  patterns = [0] + list(map(len, s2))

max_len = 1
#偶数番目+が１の人たち
lengths = [0] * (len(patterns)+1)
outs = [0] * (len(patterns)+1)
width = 2*k + 1
if width > len(patterns):
  print(len(s))
else:
  for i in range(len(lengths)):
    try:
      #print(i, len(patterns), len(lengths), len(outs))
      lengths[i+1] = lengths[i] + patterns[i]
    except Exception as e:
      pass
    if width <= i and i % 2 == 1:
       outs[i] = lengths[i] - lengths[i - width]
  print(patterns)
  print(lengths)
  print(outs)
  print(max(outs))