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)

# coding: utf-8
import sys
from bisect import bisect_left, bisect_right

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

N, K = lr()
X = lr()
if 0 in X:
    K -= 1

i = bisect_left(X, 0)
ne = X[:i]
i = bisect_right(X, 0)
po = X[i:]
INF = 10 ** 10
neg = [INF] * (K+1)  # 左からK本選ぶ場合、K-1本選ぶ場合・・・0本選ぶ場合
neg[-1] = 0
pos = [INF] * (K+1)
pos[0] = 0
for j in range(len(ne)):
    if -j-2 < -K-1:
        break
    neg[-j-2] = ne[-j-1]

for j in range(len(po)):
    if j+1 > K:
        break
    pos[j+1] = po[j]

answer = INF
for j in range(K+1):
    x = abs(neg[j]); y = abs(pos[j])
    mi = min(x, y)
    ma = max(x, y)
    temp = mi * 2 + ma
    if temp < answer:
        answer = temp
print(answer)
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