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: Time Limit Exceeded)

# -*- coding: utf-8 -*-

from math import floor

def main():
    n, k = map(int, input().split())
    xs = list(map(int, input().split()))

    if n == k:
        print(abs(xs[-1] - xs[0] + min(abs(xs[0]), abs(xs[-1]))))
        return

    min_time = 1e9
    origin = get_origin(xs, n)

    if origin <= 0:
        print(xs[k - 1])
    elif origin >= n - 1:
        print(abs(xs[-k]))
    else:
        for i in range(max(origin - k + 1, 0), min(origin + 1, n - k)):
            part = xs[i:i + k]
            time = abs(part[-1] - part[0]) + min(abs(part[0]), abs(part[-1]))
            min_time = min(time, min_time)

        print(time)


def get_origin(xs, n):
    if xs[0] == 0:
        return 0
    elif xs[0] > 0:
        return -1
    elif xs[-1] < 0:
        return n
    else:
        l = 0
        r = n
        while True:
            if r - l < 10:
                for i in range(l, r):
                    if xs[i] == 0 or xs[i + 1] > 0:
                        return i

            m = floor((r - l) / 2 + l)
            if xs[m] == 0:
                return m
            elif xs[m] < 0:
                if m < n and xs[m + 1] > 0:
                    return m
                else:
                    l = m
            else:
                if m > 0 and xs[m - 1] < 0:
                    return m - 1
                else:
                    r = m


if __name__ == '__main__':
    main()