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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>

typedef long long ll;

using namespace std;

int main(void) {
  int N, K; cin >> N >> K;
  vector<int> x(N);
  for (int i = 0; i < N; i++) { cin >> x[i]; }

  int d = INT_MAX;
  for (int i = 0; i < N - K + 1; i++) {
    int vmax = INT_MIN;
    int vmin = INT_MAX;
    for (int j = i; j < i + K; j++) {
      vmax = max(vmax, x[j]);
      vmin = min(vmin, x[j]);
    }
    int cr = abs(vmax) + abs(vmax - vmin);
    int cl = abs(vmin) + abs(vmax - vmin);
    d = min(d, min(cr, cl));
  }
  cout << d << endl;
}