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: Time Limit Exceeded)

N, K = map(int, input().split())
s = input()

t = []
cur = s[0]
cnt = 0
for ss in s:
    if cur == ss:
        cnt += 1
    else:
        sgn = 1 if cur == '1' else -1
        # 逆立ちでないなら-1
        t.append(cnt * sgn)

        cur = ss
        cnt = 1
sgn = 1 if cur == '1' else -1
# 逆立ちでないなら-1
t.append(cnt * sgn)

M = len(t)
ans = 0
for i in range(M):
    cnt = 0
    b = 0
    for j in range(i, M):
        if t[j] < 0:
            cnt += 1
            if cnt > K:
                break
            b += -t[j]
        else:
            b += t[j]
    ans = max(ans, b)
print(ans)