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)

n, k = list(map(int, input().split()))
s = input()
 
data = []
cnt = 0
curr = '1'
for i in range(len(s)):
    if s[i] != curr:
        data.append(cnt)
        curr = s[i]
        cnt = 1
    else:
        cnt += 1
data.append(cnt)
data.append(0)
data.append(0)
 
current_sum = sum(data[0:0 + 2*k+1])
ret = current_sum
for start in range(2, len(data)-k-2, 2):
    if start + 2*k >= len(data):
        break
    diff = -data[start-2]-data[start-1]+data[start + 2*k]+data[start + 2*k-1]
    current_sum += diff
 
#     print(start, val)
    if current_sum > ret:
        ret = current_sum
print(ret)