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: Wrong Answer)

N, K = map(int, input().split())

X = list(map(int, input().split()))


def calc_time(X):
    x_max = X[-1]
    x_min = X[0]

    if x_max * x_min >= 0:
        if abs(x_max) > abs(x_min):
            return x_max
        else:
            return abs(x_min)
    else:
        return x_max - x_min + min(abs(x_max), abs(x_min))

def calc_start_and_goal_position(index):
    if index - K >= 0:
        start_index = index - K
    else:
        start_index = 0
    
    if N > index + K:
        goal_index = index
    else:
        goal_index = N - K + 1
    
    return start_index, goal_index

if __name__ == "__main__":
    index = -1
    for i, x in enumerate(X):
        if x >= 0:
            index = i 
    if index == -1:
        index = i
    
    start_index, goal_index = calc_start_and_goal_position(index)

    time_min = float('inf')
    for i in range(start_index, goal_index):
        time = calc_time(X[i:i+K])
        if time < time_min:
            time_min = time

    print(time_min)