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 = map(int, input().split())
s = input()
num_list = []
know = []

for i in range(len(s)):
    num_list.append(s[i])
    if (i == 0) or (num_list[i] != num_list[i-1]):
        know.append(1)
    elif num_list[i] == num_list[i-1]:
        know[-1] += 1
print(num_list)
print(know)

length = []
if (num_list[0] == '1') and (num_list[-1] == '1'):
    for i in range(0, int((len(know)-1)/2), 2):
        if i + (k * 2) < len(know):
            length.append(sum(know[i: i + (k * 2) + 1]))
        else:
            length.append((sum(know[i:])))
        i += 1
elif (num_list[0] == '1') and (num_list[-1] == '0'):
    for i in range(0, int(len(know)/2), 2):
        if know[i+1] == know[-1]:
            length.append(know[i] + know[i+1])
        else:
            if i + (k * 2) < len(know):
                length.append(sum(know[i: i + (k * 2) + 1]))
            else:
                length.append((sum(know[i:])))
        i += 1
elif (num_list[0] == '0') and (num_list[-1] == '1'):
    for i in range(0, int(len(know)/2), 2):
        if i == 0:
            if i + (2*k) <= len(know):
                length.append(sum(know[i: i + (2*k)]))
            else:
                length.append(sum(know[i:]))
        else:
            if i + (k * 2) < len(know):
                length.append(sum(know[i: i + (k * 2) + 1]))
            else:
                length.append((sum(know[i:])))
            i += 1
elif (num_list[0] == '0') and (num_list[-1] == '0'):
    for i in range(0, int((len(know)+1)/2), 2):
        if i == 0:
            if i == 0:
                if i + (2 * k) <= len(know):
                    length.append(sum(know[i: i + (2 * k)]))
                else:
                    length.append(sum(know[i:]))
        elif know[i+1] == know[-1]:
            length.append(know[i] + know[i+1])
        else:
            if i + (k * 2) < len(know):
                length.append(sum(know[i: i + (k * 2) + 1]))
            else:
                length.append((sum(know[i:])))
            i += 1


print(max(length))