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)

from collections import defaultdict

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

left = defaultdict(int)
right = defaultdict(int)
index = 0
for i in range(1, N):
    if S[i-1] == 0 and S[i] == 1:
        right[index] = i
        index += 1
    elif S[i-1] == 1 and S[i] == 0:
        left[index] = i-1

    if i == N-1:
        if S[i] == 0:
            right[index] = i
            left[index+1] = i
        if S[i] == 1:
            left[index] = i

ans = 1
for ind in range(index+1):
    a = left[ind+1] - right[ind-K] + 1
    if ans < a:
        ans = a

print(ans)