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: Wrong Answer)

from collections import deque

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

hoge = deque()

now = int(S[0])
Sum = 1
for i in range(1, N):
    if now == int(S[i]):
        Sum += 1
    else:
        hoge.append(Sum)

        Sum = 1
        now = (now + 1) % 2

    if i == N - 1:
        hoge.append(Sum)

if N == 1:
    hoge.append(1)

rui = deque()
rui.append(0)
Sum = 0

for i in range(len(hoge)):
    Sum += hoge[i]
    rui.append(Sum)

first = int(S[0])
max = max(rui)

for i in range(first, len(rui), 2):

    if 2 * K + i == len(rui):
        i -= 1
    elif 2 * K + i > len(rui):
        break

    if rui[2 * K + i] - rui[i - first] > max:
        max = rui[2 * K + i] - rui[i - first]

    print(rui[2 * K + i] - rui[i - first])

print(max)