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 = list(input())

seq = []
tmp = 0
for i in range(N-1):
    if S[i] != S[i+1]:
        tmp += 1
        seq.append(tmp)
        tmp = 0
            
    else:
        tmp += 1

seq.append(tmp+1)

seq_sum = [0 for _ in range(len(seq)+1)]

for i in range(len(seq)):
    seq_sum[i+1] = seq_sum[i] + seq[i]

res = 1
if S[0] == '0':
    for i in range(len(seq_sum) - 2 * K - 1):
        if i%2 == 0:
            r = min(i + 2*K, len(seq_sum))
            res = max(res, seq_sum[r] - seq_sum[i]) 
        else:
            r = min(i + 2*K+1, len(seq_sum))
            res = max(res, seq_sum[r] - seq_sum[i])
        
else:
    for i in range(len(seq_sum) - 2 * K - 1):
        if i%2 == 0:
            r = min(i + 2*K+1, len(seq_sum))
            res = max(res, seq_sum[r] - seq_sum[i])
        else:
            r = min(i + 2*K, len(seq_sum))
            res = max(res, seq_sum[r] - seq_sum[i]) 
 


print(res)