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 <bits/stdc++.h>
using namespace std;
using i64 = long long;
#define rep(i,s,e) for(int (i) = (s);(i) <= (e);(i)++)
#define all(x) x.begin(),x.end()

int N,K;

int main(){
  cin >> N >> K;
  vector<int> a(N);
  rep(i,0,N - 1){
    cin >> a[i];
  }

  vector<int> pp,nn;
  rep(i,0,N - 1){
    if(a[i] >= 0){
      pp.push_back(a[i]);
    }
    else{
      nn.push_back(a[i]);
    }
  }
  sort(all(pp));
  sort(all(nn));
  reverse(all(nn));
  i64 ans = 1e18;
  for(int i = 0;i <= K;i++){
    int j = K - i;
    if(i > pp.size() || j > nn.size()) continue;
    int left = (j == 0) ? 0 : abs(nn[j - 1]);
    int right = (i == 0) ? 0 : pp[i - 1];
    i64 res = min(left * 2 + right , left + right * 2);
    ans = min(ans , res);
  }
  cout << ans << endl;
}