Codeforces Round #415 (Div. 2)-C. Do you want a date?

原题链接

C. Do you want a date?

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Leha decided to move to a quiet town Vičkopolis, because he was tired by living in Bankopolis. Upon arrival he immediately began to expand his network of hacked computers. During the week Leha managed to get access to n computers throughout the town. Incidentally all the computers, which were hacked by Leha, lie on the same straight line, due to the reason that there is the only one straight street in Vičkopolis.

Let's denote the coordinate system on this street. Besides let's number all the hacked computers with integers from 1 to n. So the i-th hacked computer is located at the point xi. Moreover the coordinates of all computers are distinct.

Leha is determined to have a little rest after a hard week. Therefore he is going to invite his friend Noora to a restaurant. However the girl agrees to go on a date with the only one condition: Leha have to solve a simple task.

Leha should calculate a sum of F(a) for all a, where a is a non-empty subset of the set, that consists of all hacked computers. Formally, let's denote A the set of all integers from 1 to n. Noora asks the hacker to find value of the expression . Here F(a) is calculated as the maximum among the distances between all pairs of computers from the set a. Formally, . Since the required sum can be quite large Noora asks to find it modulo 109 + 7.

Though, Leha is too tired. Consequently he is not able to solve this task. Help the hacker to attend a date.

Input

The first line contains one integer n (1 ≤ n ≤ 3·105) denoting the number of hacked computers.

The second line contains n integers x1, x2, ..., xn (1 ≤ xi ≤ 109) denoting the coordinates of hacked computers. It is guaranteed that all xi are distinct.

Output

Print a single integer — the required sum modulo 109 + 7.

Examples

input

2
4 7

output

3

input

3
4 3 1

output

9

将数组从小到大排序后，若集合中最小的数位d[i], 最大的数位d[j], 则这样的集合有2^(j-i-1)个

#include 
#define maxn 300005
#define MOD 1000000007
using namespace std;
typedef long long ll;

ll d[maxn];
int main() {
	//freopen("in.txt", "r", stdin);
	ll mm = (MOD + 1) / 2;
	int n;
	scanf("%d", &n);
	for(int i = 0; i < n; i++)
	 scanf("%I64d", d+i);
	sort(d, d+n);
	ll k = 1, p = 0, f = 0;
	for(int i = 0; i <= n - 2; i++) {
		(p += k) %= MOD;
		(f += d[i+1] * k % MOD) %= MOD;
		(k <<= 1) %= MOD;
	}
	ll ans = 0;
	for(int i = 0; i <= n-2; i++) {
		ans += ((f - p * d[i]) % MOD + MOD) % MOD;
		ans %= MOD;
		p--;
		(p += MOD) %= MOD;
		(p *= mm) %= MOD;
		f -= d[i+1];
		f += MOD;
		f %= MOD;
		(f *= mm) %= MOD;
	}
	cout << ans << endl;
	return 0;
}