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 <iostream> // cin, cout, cerr
#include <algorithm> // minmax, sort, swap
#include <numeric> // iota
#include <cstdio> // printf, scanf
#include <string> // string, stoi, to_string
#include <vector> // vector
#include <queue> // queue, priority_queue
#include <deque> // deque
#include <map> // key-value pairs sorted by keys
#include <set> // set
#include <iomanip> // cout<<setprecision(n)
#include <functional> // function<void(int)>

#define rep(i,n) for(int i = 0; i < (n); i++)
#define ENDL '\n'
#define print(i) std::cout << (i) << '\n'

#define int long long // at least int64 > 9*10^18
#define all(v) (v).begin(), (v).end()
/* libraries */

constexpr int MOD = 1e9+7;
struct mint
{
	int v;
	mint():v(0){}
	mint(int v):v((v+MOD)%MOD){}
	mint operator-()const{ return mint(0) - *this; }
	mint& operator+=(const mint& a){ if((v+=a.v)>=MOD) v-=MOD; return *this; }
	mint& operator-=(const mint& a){ if((v+=MOD-a.v)>=MOD) v-=MOD; return *this; }
	mint& operator*=(const mint& a){ (v*=a.v)%=MOD; return *this; }
	mint& operator/=(const mint& a){ (*this) *= a.inv(); return *this; }
	mint operator+(const mint& a)const{ return mint(*this) += a; }
	mint operator-(const mint& a)const{ return mint(*this) -= a; }
	mint operator*(const mint& a)const{ return mint(*this) *= a; }
	mint operator/(const mint& a)const{ return mint(*this) /= a; }
	bool operator<(const mint& a)const{ return v < a.v; }
	bool operator==(const mint& a)const{ return v == a.v; }
	mint pow(int k)const{ mint r(1),t(v); while(k){ if(k&1) r*=t; t*=t; k>>=1; } return r; }
	mint inv()const{ return pow(MOD-2); }
	static mint comb(int n, int k) {
		if(n-k<k) k=n-k;
		mint num(1), dom(1);
		for(int i=0;i<k;i++) { num*=n-i; dom*=i+1; }
		return num/dom;
	}
};
std::istream& operator>>(std::istream&i,mint&a){ int t; i>>t; a=mint(t); return i; }
std::ostream& operator<<(std::ostream&o,const mint&a){ o<<a.v; return o; }


signed main() {
	int n,m;
	std::cin >> n >> m;
	std::vector<mint> xx(n);
	std::vector<mint> yy(m);
	rep(i,n) std::cin >> xx[i];
	rep(i,m) std::cin >> yy[i];
	n--;
	m--;
	std::vector<mint> x(n);
	std::vector<mint> y(m);
	rep(i,n) {
		x[i] = xx[i+1] - xx[i];
	}
	rep(i,m) {
		y[i] = yy[i+1] - yy[i];
	}

	mint a = 0;
	{
		std::vector<mint> ac(n);
		ac[0] = x[0];
		rep(i,n-1) {
			ac[i+1] = ac[i] + x[i+1];
		}
		{
			mint sum = 0;
			for(auto c:ac) sum+=c;
			for(int i=0;i<n;i++) {
				a+=sum;
				sum-=mint(n-i)*x[i];
			}
		}
	}
	mint b = 0;
	{
		std::vector<mint> ac(m);
		ac[0] = y[0];
		rep(i,m-1) {
			ac[i+1] = ac[i] + y[i+1];
		}
		{
			mint sum = 0;
			for(auto c:ac) sum+=c;
			for(int i=0;i<m;i++) {
				b+=sum;
				sum-=mint(m-i)*y[i];
			}
		}
	}
	print(a*b);
	return 0;
}