Problem:
Score : 300 points

Problem Statement

There are N candles placed on a number line.
The i-th candle from the left is placed on coordinate x_i.
Here, x_1 < x_2 < ... < x_N holds.

Initially, no candles are burning.
Snuke decides to light K of the N candles.

Now, he is at coordinate 0.
He can move left and right along the line with speed 1.
He can also light a candle when he is at the same position as the candle, in negligible time.

Find the minimum time required to light K candles.

Constraints

1 \leq N \leq 10^5

1 \leq K \leq N

x_i is an integer.

|x_i| \leq 10^8

x_1 < x_2 < ... < x_N

Input

Input is given from Standard Input in the following format:

N K
x_1 x_2 ... x_N

Output

Print the minimum time required to light K candles.

Sample Input 1

5 3
-30 -10 10 20 50

Sample Output 1

40

He should move and light candles as follows:

Move from coordinate 0 to -10.

Light the second candle from the left.

Move from coordinate -10 to 10.

Light the third candle from the left.

Move from coordinate 10 to 20.

Light the fourth candle from the left.

Sample Input 2

3 2
10 20 30

Sample Output 2

20

Sample Input 3

1 1
0

Sample Output 3

0

There may be a candle placed at coordinate 0.

Sample Input 4

8 5
-9 -7 -4 -3 1 2 3 4

Sample Output 4

10

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

# coding: utf-8
# Your code here!

import bisect
from collections import defaultdict
import sys
sys.setrecursionlimit(int(1e6))
 
N, K = map(int, input().rstrip().split(' '))
X = sorted(list(map(int, input().rstrip().split(' '))))

i = bisect.bisect_left(X, 0)
X.insert(i, 0)

memo = defaultdict(lambda: defaultdict(lambda: -1))
 
def recursive(current_k, cost, i, left_i, right_i):
    if K == current_k:
        return cost
    if memo[current_k][i] != -1:
        return memo[current_k][i]
       
    left_cost = 1e10 
    if left_i >= 0:
        left_cost = recursive(current_k + 1, cost + X[i] - X[left_i], left_i, left_i - 1, right_i)
        
    right_cost = 1e10
    if right_i <= N:
        right_cost = recursive(current_k + 1, cost + X[right_i] - X[i], right_i, left_i, right_i + 1)
        
    min_cost = min(left_cost, right_cost)
    
    memo[current_k][i] = min_cost
    
    return min_cost
    
print(recursive(0, 0, i, i - 1, i + 1))