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: Wrong Answer)

N, K = map(int, input().split())
s = input() + "#"

pre, cons, comp = '#', 0, [(0, -1)]
for i in range(len(s)):
    if pre != '#' and pre != s[i]:
        if cons > 0:
            print(cons, s[i-1])
            comp.append((cons, s[i-1]))
            cons = 1
    else:
        cons += 1

    pre = s[i]

acc = [0 for _ in range(len(comp))]
for i in range(1, len(comp)):
    acc[i] = acc[i-1] + comp[i][0]

ans = 0
for i in range(len(comp) - 1):
    lim = len(comp) - 1
    if comp[i+1][1] == '1':
        lim = min(lim, i + 2*K + 1)
    else:
        lim = min(lim, i + 2*K)
    # print("i = {}, lim = {}".format(i, lim))
    ans = max(ans, acc[lim] - acc[i])

print(ans)