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: Runtime Error)

N, K = map(int, input().split())
S = list(input())
bw = [0] * N
ind = 0
for i in range(N):
  bw[ind] += S[i] == S[i + 1]
  if S[i] != S[i + 1]:
    bw[ind] += 1
    ind += 1
ind = 0
res = 0
cumsumbw = [0] + [bw[0]] + [0] * (N - 1)
for i in range(1, N):
  cumsumbw[i + 1] = cumsumbw[i] + bw[i]
if N - 2 * K <= 0:
  print(N)
  exit(0)
for i in range(N - 2 * K):
  if S[i] == "1":
    res = max(res, cumsumbw[i + 2 * K + 1] - cumsumbw[i])
  else:
    res = max(res, cumsumbw[i + 2 * K] - cumsumbw[i])
print(res)