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 (2.7.6) (judge verdict: Accepted)

def solution(a, k):
    n = len(a)
    p, q = [0], []
    for x in a:
        if x < 0:
            q.append(-x)
        else:
            p.append(x)
    q = [0] + q[::-1]
    foo = min(p[-1], q[-1]) * 2 + max(p[-1], q[-1])
    for x in xrange(max(0, k - len(p) + 1), min(k, len(q) - 1) + 1):
        y = k - x
        foo = min(min(q[x], p[y]) * 2 + max(q[x], p[y]), foo)
    return foo

def main():
    n, k = [int(i) for i in raw_input().strip().split()]
    a = [int(i) for i in raw_input().strip().split()]
    print(solution(a, k))

if __name__ == '__main__':
    main()