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: Runtime Error)

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

L = []
R = []
before = S[0]
cnt_zero = 0
cnt_one = 0
len_l = 0
len_r = 0
for i in range(N):
    if before == '0' and S[i] == '0':
        cnt_zero += 1
    elif before == '0' and S[i] == '1':
        before = '1'
        L.append(cnt_zero)
        len_l += 1
        cnt_zero = 0
        cnt_one += 1
    elif before == '1' and S[i] == '0':
        before = '0'
        R.append(cnt_one)
        len_r += 1
        cnt_zero += 1
        cnt_one = 0
    else:
    	cnt_one += 1
if cnt_zero > 0:
    L.append(cnt_zero)
    len_l += 1

if cnt_one > 0:
	R.append(cnt_one)
	len_r += 1
ans = 0
sum_one = 0
if S[0] == '0':
	sum_one = sum(L[:K]) + sum(R[:K])
else:
	sum_one = sum(L[:K]) + sum(R[:K+1])

ans = sum_one
for i in range(len_l)[1:]:
    if i + K > len_l:
        break
    elif i + K == len_l:
        if i + K > len_r:
            sum_one += (L[K+i-1] - L[i-1] - R[i-1])
            ans = max(ans, sum_one)
            break
        else:
            sum_one += (L[K+i-1] + R[K+i] - L[i-1] - R[i-1])
            ans = max(ans, sum_one)
            break
    if S[0] == '0' and i == 1:
        sum_one += (L[K] + R[K] - L[0])
    else:
        sum_one += (L[K+i-1] + R[K+i] - L[i-1] - R[i-1])
    ans = max(ans, sum_one)
print(ans)