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)

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

sorted_X = sorted(X, key=abs)

centers = []

if sorted_X[0] == 0:
    # 0がある場合
    centers.append(X.index(0))
else:
    for x in sorted_X:
        if x > 0:
            centers.append(X.index(x))
            break

    for x in sorted_X:
        if x < 0:
            centers.append(X.index(x))
            break


edge_pairs = []
# ひだりエッジ
for center_index in centers:
    left_edge = center_index - (K - 1)
    if left_edge >= 0:
        start_left_edge_index = left_edge
        start_right_edge_index = center_index
    else:
        start_left_edge_index = 0
        start_right_edge_index = K-1

    for move in range(K):
        left_edge = start_left_edge_index + move
        right_edge = start_right_edge_index + move
        if right_edge >= N:
            break
        edge_pairs.append((left_edge, right_edge))
edge_pairs = list(set(edge_pairs))


propose = []
for (left, right) in edge_pairs:
    pos_max = 0
    neg_max = 0
    for i in range(left, right+1):
        target = X[i]
        if target > 0:
            if pos_max < target:
                pos_max = target

        if target < 0:
            if neg_max < abs(target):
                neg_max = abs(target)

    propose.append(pos_max + 2 * neg_max)
    propose.append(neg_max + 2 * pos_max)


print(min(propose))