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: Runtime Error)

N,K = (int(i) for i in input().split())
K += 2 #とれる範囲
S = input()
S = [s for s in S]
cnt = []
last = S[0]
c = 0

for s in S:
    if s == last:
        c += 1
    else:
        cnt.append(c)
        c = 1
        last = s

cnt.append(c)
cnt.extend([0,0,0])
hold = sum([cnt[n] for n in range(K+1)])
ans = [hold]
for i in range(1,len(cnt)-K):
    #right => cnt[i-1]
    #left => cnt[i+K]
    ans.append(hold-cnt[i-1]+cnt[i+K])
    hold = sum([cnt[n+i] for n in range(K+1)])
print(max(ans))