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()
para = [0]
for i, s in enumerate(S):
    if i == 0:
        para.append(1)
    else:
        if S[i] == S[i-1]:
            para[-1] += 1
        else:
            para.append(1+para[-1])
i = 0

tmpmax = 0

if S[0] == '1':
    if i + 2*k + 1 >= len(para) - 1:
        print(n)
    else:
        while i + 2*k + 1 <= len(para) - 1:
            j = i + 2*k + 1
            tmpmax = max(tmpmax, para[j] - para[i-1])
            #if para[j] - para[i-1] > tmpmax:
            #    tmpmax = para[j] - para[i]

            i += 2
        print(tmpmax)
else:
    if i + 2*k >= len(para) - 1:
        print(n)
    else:
        while i + 2*k <= len(para) - 1:
            j = i + 2*k
            if i == 0:
                tmpmax = max(tmpmax, para[j] - para[i])
                #if para[j] - para[i] > tmpmax:
                #    tmpmax = para[j] - para[i]
            else:
                tmpmax = max(tmpmax, para[j] - para[i-1])
                #if para[j] - para[i-1] > tmpmax:
                #    tmpmax = para[j] - para[i-1]

            i += 2
        print(tmpmax)