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: Wrong Answer)

N, K = map(int, input().split())
S = list(str(input()))
list = [int(s) for s in S]
L = []
if list[0] == 0:
    L.append(0)
cnt = 1
for i in range(len(list) - 1):
    if list[i] == list[i + 1]:
        cnt += 1
    else:
        L.append(cnt)
        cnt = 1
L.append(cnt)

if list[N-1] == 0:
    L.append(0)
ans = 0
for i in range((len(L) + 1)//2 - K):
    print(sum(L[(2 * i):(2 * i) + (K * 2) + 1]))
    if sum(L[(2 * i):(2 * i) + (K * 2) + 1]) > ans:
        ans = sum(L[(2 * i):(2 * i) + (K * 2) + 1])
if len(L) == 1:
    ans = max(ans, L[0])
print(ans)