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)

import sys
if sys.platform in ['ios', 'win32', 'darwin']:
	sys.stdin=open('Untitled.txt')
input = sys.stdin.readline
def INT(): return int(input())
def MAP(): return [int(x) for x in input().split()]

N, K = MAP()
S = input().rstrip()
S = [int(s) for s in S]

A = []
now = -1
l = -1
for i,s in enumerate(S):
	if now == -1:
		l = i
		now = s
	elif now == s: continue
	elif now != s:
		A.append([int(now), l, i, i-l])
		now = s
		l = i
else:
	A.append([int(now), l, i+1, i-l+1])
# print(A)

if S[0] == 1:
	left, right = 0, 2*K+1
else:
	left, right = 0, 2*K
sum_A = sum(a[3] for a in A[left:right])
# print(sum_A)

# print(A)
ans = sum_A
for i in range(1, len(A)):
	if i+1 > len(A)-2: continue
	# print(i)
	now, fr, to, ln = A[i]
	if now:
		sum_A -= A[i-1][3]
		sum_A += A[i+1][3]
		sum_A += A[i+2][3]
		ans = max(ans, sum_A)
	else:
		sum_A -= A[i-1][3]
		ans = max(ans, sum_A)
	# print(now, fr, to, sum_A)
print(ans)