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: Accepted)


import sys
from collections import deque, defaultdict
import copy
import bisect
input=sys.stdin.readline
#sys.setrecursionlimit(10 ** 9)
import math
import heapq

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

S = input()
renketu = [0]
renketu_sum = [0,0]

mozi = '1'
num = 0
for i in range(N):
	if mozi == S[i]:
		renketu[-1] += 1
		renketu_sum[-1] += 1
	else:
		renketu_sum.append(renketu_sum[-1]+1)
		renketu.append(1)
	mozi = S[i]
if len(renketu) % 2 == 0:
	renketu.append(0)
	renketu_sum.append(renketu_sum[-1])


length = 2*K + 1
if length >= len(renketu_sum):
	print(renketu_sum[-1])
else:
	max_num = 0
	for i in range(len(renketu_sum) - length):
		if i % 2 == 0:
			max_num = max(max_num, renketu_sum[i + length] - renketu_sum[i])
			#print(max_num, i, renketu,renketu_sum, length)
	print(max_num)