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 (Clang 3.8.0) (judge verdict: Accepted)


#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
#define REP(var, a, b) for (int var = (a); var < (b); var++)
#define rep(var, n) for (int var = 0; var < (n); ++var)
#define ALL(c) (c).begin(), (c).end()
#define rALL(c) (c).rbegin(), (c).rend()
ll MOD = 1000000007;
const ll INF = 1LL << 62;

struct mint {
  ll x;
  mint(ll x = 0) : x(x % MOD) {}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= MOD) x -= MOD;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += MOD - a.x) >= MOD) x -= MOD;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }

  // for prime MOD
  mint inv() const { return pow(MOD - 2); }
  mint& operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

int main() {
  //
  ll n, m;
  cin >> n >> m;
  vl x(n), y(m);
  rep(i, n) { cin >> x[i]; }
  rep(i, m) { cin >> y[i]; }
  sort(ALL(x));
  sort(ALL(y));

  mint xsum(0);
  rep(i, n - 1) {
    mint len(x[i + 1] - x[i]);
    xsum = xsum + len * mint(i + 1) * mint(n - (i + 1));
  }
  // cerr << xsum.x << endl;

  mint ysum(0);
  rep(i, m - 1) {
    mint len(y[i + 1] - y[i]);
    ysum = ysum + len * mint(i + 1) * mint(m - (i + 1));
  }

  mint ans = xsum * ysum;
  cout << ans.x << endl;
  return 0;
}