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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;


void solve () {
    int n, k;
    cin >> n >> k;
    vector<long long> pos, neg;
    pos.push_back(0);
    while(n--) {
        long long x;
        cin >> x;
        if (x >= 0) {
            pos.push_back(x);
        }
        else {
            neg.push_back(-1 * x);
        }
    }
    neg.push_back(0);
    reverse(neg.begin(), neg.end());
    long long ans = INT_MAX;
    for (int i = 0, j = k; i <= k; i++, j--) {
        if(i >= (int) neg.size() || j >= pos.size()) {
            continue;
        }
        if(neg[i] > pos[j]) {
            swap(neg[i], pos[j]);
        }
        ans = min(ans, (neg[i] * 2) + pos[j]);
    }
    cout <<  ans;

}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    solve();
    return 0;
}