Codeforces 810C Do you want a date?【思维】

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

34 3 1

Output

9

Note
There are three non-empty subsets in the first sample test:

,


and


. The first and the second subset increase the sum by
0 and the third subset increases the sum by
7 - 4 = 3. In total the answer is 0 + 0 + 3 = 3.

There are seven non-empty subsets in the second sample test. Among them only the following subsets increase the answer:


,


,


,


. In total the sum is
(4 - 3) + (4 - 1) + (3 - 1) + (4 - 1) = 9.

题目大意：

给你一个长度为N的序列，让你求其中所有子序列（不必要连续）的f值的加和，其一个子序列的f值是其最大值减去最小值的差。

思路：

1、因为子序列不必要连续，那么我们首先将整个序列从小到大排序。

2、然后我们枚举一个长度为5的序列的最终值：

A1,A2,A3,A4,A5

A2-A1+2(A3-A1)+4(A4-A1)+8(A5-A1);

A3-A2+2(A4-A2)+4(A5-A2);

A4-A3+2(A5-A3);

A5-A4;

整理得到：

-15A1-7A2-3A3-A4

+A2+3A3+7A4+15A5.

那么不难看出其中的规律，只要注意减法取模即可。

Ac代码：

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
#define ll __int64
ll mod=1e9+7;
ll a[300050];
int main()
{
int n;
while(~scanf("%d",&n))
{
ll output=0;
for(int i=1;i<=n;i++)scanf("%I64d",&a[i]);
sort(a+1,a+1+n);
ll sum=0;
ll now=1;
for(int i=2;i<=n;i++)
{
sum+=now;
sum%=mod;
now*=2;
now%=mod;
output+=a[i]*sum;
output%=mod;
}
sum=0;
now=1;
for(int i=n-1;i>=1;i--)
{
sum+=now;
sum%=mod;
sum%=mod;
now*=2;
now%=mod;
output=((output-a[i]*sum)+mod)%mod;
}
printf("%I64d\n",(output+mod)%mod);
}
}