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: Accepted)

#include <bits/stdc++.h> 
using namespace std;

#ifdef LOCAL
    #define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
        #define eprintf(...) 42
#endif

#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define repi(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define all(x) (x).begin(),(x).end()
#define foreach(u,v) for(auto (u) : (v))
#define pb push_back
#define mp make_pair
#define mt make_tuple

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<ll, ll> pll;
typedef vector<ll> vl;

const int inf = 1e9;
const ll linf = 1LL<<60;
const ll mod = 1e9 + 7;
const double eps = 1e-9;

/*
*/

int main()
{
  #define int long long 

  int n, m;
  cin >> n >> m;

  vl x(n), y(m);
  rep(i, n) cin >> x[i];
  rep(i, m) cin >> y[i];

  ll sx = 0;
  rep(i, n-1){
    sx += (i+1)*(n-1-i)%mod*(x[i+1]-x[i])%mod;
    sx %= mod;
  }

  ll sy = 0;
  rep(i, m-1){
    sy += (i+1)*(m-1-i)%mod*(y[i+1]-y[i])%mod;
    sy %= mod;
  }

  cout << sx*sy%mod << endl;

  return 0;
}