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 (7.3.0) (judge verdict: Runtime Error)

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

if N == 1:
  if S == '1':
    print(1)
  elif K > 0:
    print(1)
  else:
    print(0)
  exit()

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

if S[0] == '1':
  ans = sum(l[:2*K+1])
  tmp = sum(l[:2*K+1])
  if S[-1] == '1':
    for i in range(0, len(l)-2*K-2, 2):
      tmp += l[2*K+i+1] + l[2*K+i+2] - l[i] - l[i+1]
      ans = max(ans, tmp)
  else:
    for i in range(0, len(l)-2*K-2, 2):
      tmp += l[2*K+i+1] + l[2*K+i+2] - l[i] - l[i+1]
      ans = max(ans, tmp)
    tmp += l[2*K+i+1] - l[i] - l[i+1]
    ans = max(ans, tmp)
else:
  ans = max(sum(l[:2*K]), sum(l[1:2*K+2]))
  tmp = sum(l[1:2*K+2])
  if S[-1] == '1':
    for i in range(1, len(l)-2*K-2, 2):
      tmp += l[2*K+i+1] + l[2*K+i+2] - l[i] - l[i+1]
      ans = max(ans, tmp)
  else:
    for i in range(1, len(l)-1, 2):
      tmp += l[2*K+i+1] + l[2*K+i+2] - l[i] - l[i+1]
      ans = max(ans, tmp)
    tmp = sum(l[-2*K:])
    ans = max(ans, tmp)
print(ans)