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 (3.8.2) (judge verdict: Accepted)

def run_length_compress(S):
    res = [[S[0], 1]]
    for c in S[1:]:
        if c == res[-1][0]:
            res[-1][1] += 1
        else:
            res.append([c, 1])
    return res


N, K = map(int, input().split())
S = input()
cs = run_length_compress(S)
M = len(cs)

ans = 0
tot = 0
right = 0
zeros = 0
for left in range(M):
    while right < M and zeros + (cs[right][0] == "0") <= K:
        if cs[right][0] == "0":
            zeros += 1
        tot += cs[right][1]
        right += 1

    ans = max(ans, tot)

    if left == right:
        right += 1
    else:
        if cs[left][0] == "0":
            zeros -= 1
        tot -= cs[left][1]
print(ans)