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 ton 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 from1 to n. So thei-th hacked computer is located at the pointx_i. 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 alla, where a is a non-empty subset of the set, that consists of all hacked computers. Formally, let's denoteA the set of all integers from 1 to n. Noora asks the hacker to find value of the expression. HereF(a) is calculated as the maximum among the distances between all pairs of computers from the seta. 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, ..., x_n(1 ≤ x_i ≤ 10⁹) denoting the coordinates of hacked computers. It is guaranteed that allx_i are distinct.

Output

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

Examples

Input

24 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 by0 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 __int64ll 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);    }}