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)

import sys
N, K = map(int, input().split())
x = list(map(int, input().split()))

def fast(x, y):
  return min(abs(x), abs(y)) + abs(x) + abs(y)

n = N
for k in range(N):
  if x[k] >= 0:
    n = k
    if x[k] == 0:
      K -= 1
      N -= 1
      x.pop(k)
    break

if n == 0:
  if K == 0:
    print(0)
    sys.exit()
  print(x[K-1])
  sys.exit()

if n == N:
  print(x[N-K])
  sys.exit()

time = 2*10**8 + 100
if (n-K) >= 0:
  time = abs(x[n-K])
for j in range(K-n-1, N-n):
  time = min(time, fast(x[n-K+1+j], x[n+j]) )
if n + K <= N:
  time = min(time, abs(x[n+K-1]))

print(time)