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 (3.4.3) (judge verdict: Accepted)

N, K = map(int, input().split())
S = input()
left = 0
rc = 0
rf = False
lf = False
ans = 0
if set(S) == set("0") or set(S) == set("1"):
    print(len(S))
    exit()
for right in range(N):
    if rf and S[right] == "0" and rc <= K:
        if right != N-1:
            continue
        else:
            ans = max(ans, right - left)
            break
    if S[right] == "1":
        rf = False
    if S[right] == "0":
        rc += 1
        rf = True
    if rc > K:
        while True:
            if S[left] == "1":
                left += 1
            if S[left] == "0":
                while S[left] == "0":
                    left += 1
                break
        rc -= 1
    ans = max(ans, right - left)
print(ans+1)