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)

INF = 10**9
N, K = map(int, input().split())
s = input().split()
mc = []
pc = []
for i in s:
  c = int(i)
  if c==0:
    K -= 1
  if c<0:
    mc += [-c]
  elif c>0:
    pc += [c]

mc.sort()
pc.sort()
mc += [INF]
pc += [INF]

m = K
xi = -1
yi = -1
while m>0:
  if pc[xi+1]>2*mc[yi+1]:
    yi += 1
  else:
    xi += 1
  m -= 1
if yi!=-1:
  c1 = pc[xi] + 2*mc[yi]
else:
  c1 = pc[xi]

m = K
xi = -1
yi = -1
while m>0:
  if mc[yi+1]>2*pc[xi+1]:
    xi += 1
  else:
    yi += 1
  m -= 1
if xi!=-1:
  c2 = 2*pc[xi] + mc[yi]
else:
  c2 = mc[xi]

if K==0:
  print(0)
else:
  print(min(c1, c2))