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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(){
  int i, n, k, n_m = 0, n_p = 0;
  int x_m[ 100001 ] = {0};
  int x_p[ 100001 ] = {0};

  scanf( "%d%d", &n, &k );
  for ( i = 0; i < n; i++ ){
    int temp;
    scanf( "%d", &temp );
    if ( temp < 0 ){
      x_m[ n_m ] = temp;
      n_m++;
    }else {
      x_p[ n_p ] = temp;
      n_p++;
    }
  }
  //printf( "%d %d\n", n_m, n_p );
  int dist = -1, k_m = 0, k_p = k - k_m;
  int temp_d;
  //int pattern = 0;
  do{
    
    if ( k_p > n_p || k_m > n_m ){
      k_m++;
      k_p = k - k_m;
      continue;
    }
    //printf( "%d %d\n", k_m, k_p );
    temp_d = 0;
    if ( k_p == 0 ){
      //printf( "%d \n", x_m[ n_m - k_m ] );
      temp_d = ( -1 ) * x_m[ n_m - k_m ];
      //printf( "a:%d %d\n", temp_d, dist );
      if ( dist < 0 || dist > temp_d ) dist = temp_d;
    }else if ( k_m == 0 ){
      //printf( " %d\n", x_p[ k_p - 1 ] );
      temp_d = x_p[ k_p - 1 ];
      //printf( "b:%d %d\n", temp_d, dist );
      if ( dist < 0 || dist > temp_d ) dist = temp_d;
    }else if ( ( -1 ) * x_m[ n_m - k_m ] < x_p[ k_p - 1 ] ){
      //printf( "%d %d\n", x_m[ n_m - k_m ], x_p[ k_p - 1 ] );
      temp_d = -2 * x_m[ n_m - k_m ] + x_p[ k_p - 1 ];
      //printf( "c:%d %d\n", temp_d, dist );
      if ( dist < 0 || dist > temp_d ) dist = temp_d;
    }else if( ( -1 ) * x_m[ n_m - k_m ] >= x_p[ k_p - 1 ] ){
      //printf( "%d %d\n", x_m[ n_m - k_m ], x_p[ k_p - 1 ] );
      temp_d = ( -1 ) * x_m[ n_m - k_m ] + 2 * x_p[ k_p - 1 ];
      //printf( "d:%d %d\n", temp_d, dist );
      if ( dist < 0 || dist > temp_d ) dist = temp_d;
    }
    k_m++;
    k_p = k - k_m;
  }while ( k_m <= k );

  printf( "%d\n", dist );

  return 0;
}