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>
#ifdef _WIN32
#include "debug.hpp"
#endif
using namespace std;

#define rep(i, N)  for(int i = 0; i < (N); i++)
#define reps(i, N) for(int i = 1; i <= (N); i++)
#define repr(i, N) for(int i = (N) - 1; i >= 0; i--)
#define pub push_back

template<typename T> 
void chmax(T &a, T b){ a = max(a, b); };
template<typename T> 
void chmin(T &a, T b){ a = min(a, b); };

typedef long long ll;
typedef pair<int, int> P;
const int INF = 100000000;
const ll LINF = 10000000000000000;
const int MOD = 1000000007;
const int dx[9] = { 0, 1,  0, -1, 1,  1, -1, -1, 0};
const int dy[9] = { 1, 0, -1,  0, 1, -1, -1,  1, 0};
//--------------------------------------//
int n, m;
ll x[100000], y[100000];

ll xs[100000];
ll sy;
void solve(){
	ll ans = 0;
	rep(i, n - 1)
		xs[i] = ((x[i + 1] - x[i]) * (i + 1) * (n - i - 1)) % MOD;
	rep(i, m - 1)
		sy = (sy + (y[i + 1] - y[i]) * (i + 1) * (m - i - 1)) % MOD;
	rep(i, n - 1)
		ans = (ans + xs[i] * sy) % MOD;
	cout<<ans<<endl;
}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cin >> n >> m;
	rep(i, n)
		cin >> x[i];
	rep(i, m)
		cin >> y[i];
	solve();
	return 0;
}