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)

inf = float('inf')

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

m, p = [], []
for xx in x:
    if xx > 0:
        p.append(xx)
    elif xx < 0:
        m.append(-xx)
    else:
        K -= 1
        if K == 0:
            print(0)
            exit()
m.sort()
lp = len(p)
lm = len(m)

ans = inf
for from_minus in range(min(lm, K) + 1):
    from_plus = K - from_minus
    if from_plus > lp:
        continue
    if from_minus == 0:
        ans = min(ans, p[K - 1])
    elif from_minus == K:
        ans = min(ans, m[K - 1])
    else:
        ans = min(ans, p[from_plus - 1] * 2 + m[from_minus - 1])
        ans = min(ans, m[from_minus - 1] * 2 + p[from_plus - 1])
print(ans)