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: Runtime Error)

import sys
input = lambda: sys.stdin.readline().rstrip()
from itertools import accumulate


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

S = input()

if len(S) == 1:
    print('1')
    exit()

cum_sum = [0]

tmp_S = S

if S[-1] == '0':
    tmp_S += '1'
else:
    tmp_S += '0'

cnt = 1
for i in range(len(tmp_S)-1):
    if tmp_S[i] == tmp_S[i+1]:
        cnt += 1
    else:
        cum_sum.append(cnt)
        cnt = 1

print(*cum_sum)
cum_sum = list(accumulate(cum_sum))
print(*cum_sum)

ans = 0
ran = K+K
if S[0] == '0':
    for i in range(0, len(cum_sum), 2):
        if i+ran < len(cum_sum):
            ans = max(ans, cum_sum[i+ran] - cum_sum[i])
else:
    for i in range(0, len(cum_sum), 2):
        if i+ran < len(cum_sum):
            ans = max(ans, cum_sum[i+ran+1] - cum_sum[i])

print(ans)