Problem:
Score : 500 points

Problem Statement

On a two-dimensional plane, there are m lines drawn parallel to the x axis, and n lines drawn parallel to the y axis.
Among the lines parallel to the x axis, the i-th from the bottom is represented by y = y_i.
Similarly, among the lines parallel to the y axis, the i-th from the left is represented by x = x_i.

For every rectangle that is formed by these lines, find its area, and print the total area modulo 10^9+7.

That is, for every quadruple (i,j,k,l) satisfying 1\leq i < j\leq n and 1\leq k < l\leq m, find the area of the rectangle formed by the lines x=x_i, x=x_j, y=y_k and y=y_l, and print the sum of these areas modulo 10^9+7.

Constraints

2 \leq n,m \leq 10^5

-10^9 \leq x_1 < ... < x_n \leq 10^9

-10^9 \leq y_1 < ... < y_m \leq 10^9

x_i and y_i are integers.

Input

Input is given from Standard Input in the following format:

n m
x_1 x_2 ... x_n
y_1 y_2 ... y_m

Output

Print the total area of the rectangles, modulo 10^9+7.

Sample Input 1

3 3
1 3 4
1 3 6

Sample Output 1

60

The following figure illustrates this input:

The total area of the nine rectangles A, B, ..., I shown in the following figure, is 60.

Sample Input 2

6 5
-790013317 -192321079 95834122 418379342 586260100 802780784
-253230108 193944314 363756450 712662868 735867677

Sample Output 2

835067060

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<algorithm>
#define MOD 1000000007
using namespace std;
typedef long long ll;
signed main(){
  ll n,m,xsum=0,ysum=0,ans=0;
  cin >> n >> m;
  ll tx[n],ty[m],x[n],y[n];
  for(ll i=0;i<n;i++){
    cin >> tx[i];
  }
  for(ll i=0;i<m;i++){
    cin >> ty[i];
  }
  sort(tx,tx+n);
  sort(ty,ty+m);
  n--; m--;
  for(ll i=0;i<n;i++){
    x[i]=tx[i+1]-tx[i];
  }
  for(ll i=0;i<m;i++){
    y[i]=ty[i+1]-ty[i];
  }
  for(ll i=0;i<n;i++){
    if(i==0||i==n-1){
      xsum+=x[i]*n;
    }else{
      xsum+=((i+1)*(n-i))*x[i];
    }
    xsum%=MOD;
  }
  for(ll i=0;i<m;i++){
    if(i==0||i==m-1){
      ysum+=y[i]*m;
    }else{
      ysum+=((i+1)*(m-i))*y[i];
    }
    ysum%=MOD;
  }
  ans = xsum*ysum;
  ans%=MOD;
  cout << ans<<endl;
}