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 <algorithm>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <vector>
using namespace std;
using ll = long long;
#define fst first
#define snd second

/* clang-format off */
template <class T, size_t D> struct _vec { using type = vector<typename _vec<T, D - 1>::type>; };
template <class T> struct _vec<T, 0> { using type = T; };
template <class T, size_t D> using vec = typename _vec<T, D>::type;
template <class T> vector<T> make_v(size_t size, const T& init) { return vector<T>(size, init); }
template <class... Ts> auto make_v(size_t size, Ts... rest) { return vector<decltype(make_v(rest...))>(size, make_v(rest...)); }
/* clang-format on */

int main() {
  int N, K;
  while (cin >> N >> K) {
    vector<ll> x(N);
    for (int i = 0; i < N; i++) cin >> x[i];
    int p = 0;
    while (p < N && x[p] < 0) ++p;
    ll res = 1ll << 60;
    for (int i = 0; i < N; i++) {
      if (i < p) {
        ll cost = -x[i];
        int rem = K - (p - i);
        if (rem <= 0) {
          res = min(res, cost);
        } else if (p + rem - 1 < N) {
          cost += x[p + rem - 1] - x[i];
          res = min(res, cost);
        }
      } else {
        ll cost = x[i];
        int rem = K - (i - p + 1);
        if (rem <= 0) {
          res = min(res, cost);
        } else if (p - rem >= 0) {
          cost += x[i] - x[p - rem];
          res = min(res, cost);
        }
      }
    }
    cout << res << endl;
  }
  return 0;
}