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 = input()

#K回範囲を選択して反転、を繰り返し、1の連続数を最大にする
#連続した0を１度しか含まないK+1個の1の連続を探して範囲を出力する……？

change = [0]
for i in range(1,N):
    if S[i] == '1' and S[i-1] != '1':
        change.append(i)
    elif S[i] == '0' and S[i-1] != '0':
        change.append(i)

result = 0
if S[0] == '1':
    for i, point in enumerate(change):
        if i + K*2 + 2 > len(change):
            if i % 2 == 0:
                if result < N - point:
                    result = N - point
            else:
                if result < N - point - 1:
                    result = N - point - 1
            break
        if i % 2 == 0:
            if result < change[i + 1 + K*2] - point:
                result = change[i + 1 + K*2] - point
        else:
            if result < change[i + K*2] - change[i-1]:
                result = change[i + K*2] - change[i-1]
else:
    for i, point in enumerate(change):
        if i + K*2 + 2 > len(change):
            if i % 2 == 0:
                if result < N - point - 1:
                    result = N - point - 1
            else:
                if result < N - point:
                    result = N - point
            break
        if i % 2 == 0:
            if i == 0:
                if result < change[i + K*2] - change[i]:
                    result = change[i + K*2] - change[i]
                continue
            if result < change[i + K*2] - change[i-1]:
                result = change[i + K*2] - change[i-1]
        else:
            if result < change[i + 1 + K*2] - point:
                result = change[i + 1 + K*2] - point
print(result)