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 (7.3.0) (judge verdict: Wrong Answer)

import itertools
def s(): return input()
def I(): return map(int,input().split())

N,K = I()
S = list(s())
num = 1
cnt = 0
L = []
for i in range(N-1):
    if S[i] != S[i+1]:
        L.append(num)
        num = 0
        if S[i] == 0:
            cnt += 1
    num += 1
L.append(num)
if S[-1] == '0':
    cnt += 1
ruiseki = [0]+list(itertools.accumulate(L))
l = len(ruiseki)
if cnt <= K:
    print(N)
    exit()
start = 0
ans = 0
if S[0] == '0':
    start = 1
for i in range(start,l,2):
    if i+K*2+1 > l-1:
        break
    ans = max(ans,ruiseki[i+K*2+1]-ruiseki[i])
if S[0] == '0':
    ans = max(ans,ruiseki[K*2])
if S[-1] == '0':
    ans = max(ans,ruiseki[-1]-ruiseki[l-K*2-1])
print(ans)