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())
X=[int(i) for i in input().split()]
A=[]
B=[]
for x in X:
    if x<0:
        A.append(x)
    else:
        B.append(x)
ans=10**18
a=len(A)
b=len(B)
if a==0:
    print(B[K-1])
    sys.exit()
if b==0:
    print(abs(A[-K]))
    sys.exit()
for i in range(max(1,K-b),a+1):
    if i>=K:
        ans=min(ans,abs(A[-i]))
        continue
    ans = min(ans,2*abs(A[-i])+B[K-i-1])
for i in range(max(0,K-a-1),b):
    if i>=K-1:
        ans=min(ans,abs(B[i]))
        continue
    ans=min(ans,2*abs(B[i])+abs(A[-K+i+1]))
print(ans)