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)

from sys import stdin
N,K = [int(x) for x in stdin.readline().rstrip().split()]
S = (stdin.readline().rstrip())
zero = []
one = []
tmp = 1
S += "@"

for i in range(N):
    if S[i] == S[i+1]:
        tmp += 1
    else:
        if S[i] == "0":
            zero.append(tmp)
        else:
            one.append(tmp)
        tmp = 1
        
if K >= len(zero):
    print(N)
else:
    if S[0] == "1":
        tmp = sum(zero[:K]) + sum(one[:K+1])
        ans = sum(zero[:K]) + sum(one[:K+1])

        for i in range(0,len(zero)-K):
            tmp -= zero[i]
            tmp += zero[i+K]
            tmp -= one[i]
            if not i+K+1 >= len(one):
                tmp += one[i+K+1]
            ans = max(ans,tmp)
        print(ans)
    else:
        tmp = sum(zero[:K]) + sum(one[:K])
        ans = sum(zero[:K]) + sum(one[:K])

        for i in range(0,len(zero)-K):
            tmp -= zero[i]
            tmp += zero[i+K]
            if i != 0:
                tmp -= one[i]
            if not i+K >= len(one):
                tmp += one[i+K]
            ans = max(ans,tmp)
        print(ans)