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()
lis = [0]
j = 0
if s[0] == '0':
    lis.append(0)
    j = 1
#print(len(lis))
lis[j] += 1
for i in range(1,n):
    #print(len(lis))
    if s[i] != s[i-1]:
        j += 1
        lis.append(0)
    lis[j] += 1
if s[n-1] == '0':
    lis.append(0)
#print(lis)
com = [0] * (len(lis) + 1)
for i in range(len(lis)):
    com[i+1] = com[i] + lis[i]
#print(com)
ans = 0
for i in range(len(lis)):
    if i % 2 == 0:
        ans = max(ans,lis[i])


for i in range(len(com) - (k*2+1)+1):
    if i % 2 == 1:
        continue
    val = com[i+(k*2+1)] - com[i]
    ans = max(val,ans)
print(ans)