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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)


import sys
import bisect


def parse(file):
    n, k = map(int, file.readline().split())
    candles = map(int, file.readline().strip().split())

    return n, k, candles


def main(n, k, candles):
    candles = list(candles)

    i0 = bisect.bisect_left(candles, 0)

    if i0 == 0:  # 左端
        return candles[k - 1]
    if i0 == n:  # 右端
        return abs(candles[-k])

    i1 = i0
    i2 = i1 - 1
    
    if k == 1:
        return min(candles[i1], abs(candles[i2]))

    while True:
        if i1 - i2 + 1 >= k:
            break

        if i1 == n-1:
            i2 = n - k
            break
        else:
            j1 = i1 + 1

        if i2 == 0:
            i1 = k-1
            break
        else:
            j2 = i2 - 1

        if candles[j1] >= - candles[j2]:
            i2 = j2
        else:
            i1 = j1

    v1 = candles[i1]
    v2 = abs(candles[i2])
    return min(v1, v2) * 2 + max(v1, v2)


if __name__ == '__main__':
    print(main(*parse(sys.stdin)))