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: Accepted)

#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <cmath>
#include <deque>
#include <algorithm>
#include <random>
#include <ctime>
using namespace std;

#define int int64_t
#define pb push_back
#define pbb pop_back
#define pf pop_front
#define pff push_front
#define mp make_pair
#define all(c) (c).begin(),(c).end()
#define rall(c) (c).rbegin(),(c).rend()
typedef long double ld;
typedef long long ll;
typedef pair<int, int> pii;

const int INF = 1e12, MOD = 1e9 + 7, MAXN = 1e5 + 7, MAX = 5;
const ld EPS = 1e-9, PI = acos(-1);

int32_t main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cout << fixed;
    cout.precision(10);

    int n, k;
    cin >> n >> k;
    vector<int> nums(n);
    for (int i = 0; i < n; ++i)
        cin >> nums[i];

    vector<int> neg, pos;
    for (int i = 0; i < n; ++i) {
        if (nums[i] < 0)
            neg.pb(nums[i]);
        else if (nums[i] == 0)
            k--;
        else
            pos.pb(nums[i]);
    }

    if (k == 0) {
        cout << 0 << endl;
        return 0;
    }

    int ans = INF;
    if (neg.size() >= k)
        ans = min(ans, abs(neg[neg.size() - k]));
    if (pos.size() >= k)
        ans = min(ans, pos[k - 1]);
    for (int now = max((int)0, (int)(neg.size() - k + 1)); now < neg.size() && k - (neg.size() - now) <= pos.size(); ++now) {
        //cout << now << " " << k - (neg.size() - now) - 1 << " " << neg[now] << " " << pos[k - (neg.size() - now) - 1] << endl;
        ans = min(ans, abs(neg[now]) + pos[k - (neg.size() - now) - 1] + min(abs(neg[now]), pos[k - (neg.size() - now) - 1]));
    }

    cout << ans << endl;

    return 0;
}