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()

x = []
idx = 0
b = 1
while idx<n:
    st = idx
    while idx<n and int(s[idx])==b:
        idx += 1
    x.append(idx-st)
    st = idx
    b ^= 1

if b == 1:
    x.append(0)

ans = n
if len(x) > 2*k+1:
    ans = 0

    t = 0
    for i in range(2*k+1):
        t += x[i]
    ans = max(ans, t)

    for i in range(2*k+1, len(x), 2):
        t -= x[i - (2*k+1)]
        t -= x[i+1 - (2*k+1)]
        t += x[i]
        t += x[i+1]
        ans = max(ans, t)

print(ans)