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 = list(map(int, input().split()))
S = input()

L = [[0, 0]]
re = S[0]
for i in range(1, len(S)):
  if S[i] != re:
    re = S[i]
    L[-1][1] = i
    L.append([i, 0])
l = len(L)
L[-1][1] = N

if S[0] == "0":
  z = (l // 2) + 1
else:
  z = (l + 1) // 2
  
if z <= K:
  print(N)
  exit()

ma = 0
if S[0] == "0":
  ma = max(ma, L[K * 2 - 1][1])
  s = 1
else:
  s = 0
if S[-1] == "0":
  ma = max(ma, N - L[-K * 2][0])

t = K * 2
for i in range(s, l - t, 2):
  ma = max(ma, L[t + i][1] - L[i][0])
print(ma)