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;
typedef long long int ll;
#define rep( i, n, m ) for(int i = ( n ); i < ( m ); i++)
#define rep_d( i, n, m ) for(int i = ( n ) - 1; i >= ( m ); i--)
#define sort_asc( X ) sort(( X ).begin(), ( X ).end())
#define sort_desc( X ) sort(( X ).begin(), ( X ).end(), greater <>())

template <class T> bool chmax( T& a, T b );
template <class T> bool chmin( T& a, T b );
int* eratosthenes( int N );
bool bit_search( int pattern, int N );
template <class T> void cumulative_sum( T array, size_t N );

const ll INF = 1LL << 60;
const int k_mod = 1e9 + 7;

template <typename T, typename K> struct P {
	T a; K b;
};
typedef struct {
	vector <int> to;
	bool is_visited = false;
} node;
typedef struct {
	int to;
	int cost;
	P <int, int> change;
} edge;
int main( void ){
	int N, K; cin >> N >> K;
	vector <int> vec( N + 1 ), input( N );
	rep( i, 0, N ){
		cin >> input[ i ];
	}
	vec[ 0 ] = 0;
	rep( i, 0, N ){
		vec[ i + 1 ] = vec[ i ] + input[ i ];
	}
	int ans = k_mod;
	rep( i, 0, N - K + 1 ){
		ans = min( ans, input[ i + K-1 ] - input[ i ] + min( abs( input[ i ] ), abs( input[ i + K-1 ] )));
	}
	cout << ans << endl;

}

int* eratosthenes( int N ){
	int* prime_array = new int[ N + 1 ];
	int lim = N;
	prime_array[ 0 ] = 0;
	prime_array[ 1 ] = 0;
	rep( i, 2, N + 1 ){
		prime_array[ i ] = 1;
	}
	rep( i, 2, lim ){
		if (prime_array[ i ] == 0)
			continue;
		lim = N / i;
		for(int j = i * 2; j < N + 1; j += i){
			prime_array[ j ] = 0;
		}
	}
	return prime_array;
}
template <class T> void cumulative_sum( T array, size_t N ) {
	rep( i, 1, N + 1 ){
		array[ i ] += array[ i - 1 ];
	}
}
template <class T> bool chmax( T& a, T b ) {
	if (a < b){
		a = b; return true;
	}
	return false;
}
template <class T> bool chmin( T& a, T b ) {
	if (a > b){
		a = b; return true;
	}
	return false;
}
bool bit_search( int pattern, int N ){
	int cnt = 0;
	rep( bit, 0, N ){
		if (pattern & ( 1 << bit )){
			cnt++;
		}
	}
	return true;
}