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: Accepted)

import sys
N,K = map(int,input().split())
Data = list(map(int,input().split()))
Move = K
if 0 in Data:
    Move -= 1
Pos = []
Neg = []
for d in Data:
    if d > 0:
        Pos.append(d)
    if d < 0:
        Neg.append(-d)
Pos.sort()
Neg.sort()
posMaxRange = min(Move,len(Pos))
negMaxRange = min(Move,len(Neg))

if Move == 0:
    print(0)
    sys.exit()

minlen = -1
for t in range(1,posMaxRange+1):
    distance  = Pos[t-1]
    left = Move-t
    if left > 0:
        if len(Neg) < left:
            continue
        distance += Pos[t-1]
        distance += Neg[left-1]

    if minlen == -1:
        minlen = distance
    else:
        if minlen > distance:
            minlen = distance

for t in range(1,negMaxRange+1):
    distance = Neg[t-1]
    left = Move - t
    if left > 0:
        if len(Pos) < left:
            continue
        distance += Neg[t-1]
        distance += Pos[left-1]

    if minlen == -1:
        minlen = distance
    else:
        if minlen > distance:
            minlen = distance

print(minlen)