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;
int k, n, m, a[100005], sum[100005], ans = (1<<30), b[100005], n1, n2;
int cmp(int x, int y){
	return abs(x) < abs(y);
}
int main(){
	scanf("%d%d", &n, &m);
	for(int i = 1; i <= n ; i++){
		scanf("%d", &k);
		if(k == 0) m --;
		else
		if(k < 0) a[++n1] = k;
		else b[++n2] = k;	
	}
	if(m <= 0) {printf("0");return 0;}
	sort(a + 1, a + 1 + n1, cmp);
	sort(b + 1, b + 1 + n2, cmp);
	for(int i = max(0, m - n2); i <= min(n1, m); i++){
		int j = m - i;
		if(- a[i] * 2 + b[j] < ans) ans = - a[i] * 2 + b[j];
	}
	for(int i = max(0, m - n1); i <= min(n2, m); i++){
		int j = m - i;
		if(b[i] * 2 - a[j] < ans) ans = b[i] * 2 - a[j];
	}
	printf("%d", ans);
	return 0;
}