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;
constexpr int64_t mod = 1'000'000'007;
template <uint32_t mod>
class modint{
    uint64_t value;
public:
    constexpr modint(const int64_t x=0) noexcept: value(x % mod + (x < 0 ? mod : 0)){ }
    constexpr explicit operator uint64_t() const noexcept{ return value; }
    constexpr modint inverse() const noexcept{ return pow(*this, mod-2); }
    constexpr bool operator==(const modint &rhs) const noexcept{ return value == rhs.value; }
    constexpr bool operator!=(const modint &rhs) const noexcept{ return value != rhs.value; }
    constexpr modint operator+() const noexcept{ return modint(*this); }
    constexpr modint operator-() const noexcept{ return modint(mod - value); }
    constexpr modint operator+(const modint &rhs) const noexcept{ return modint(*this) += rhs; }
    constexpr modint operator-(const modint &rhs) const noexcept{ return modint(*this) -= rhs; }
    constexpr modint operator*(const modint &rhs) const noexcept{ return modint(*this) *= rhs; }
    constexpr modint operator/(const modint &rhs) const noexcept{ return modint(*this) /= rhs; }
    constexpr modint &operator+=(const modint &rhs) noexcept{
        if((value += rhs.value) >= mod) value -= mod;
        return *this;
    }
    constexpr modint &operator-=(const modint &rhs) noexcept{ return *this += mod - rhs.value; }
    constexpr modint &operator*=(const modint &rhs) noexcept{
        if((value *= rhs.value) >= mod) value %= mod;
        return *this;
    }
    constexpr modint &operator/=(const modint &rhs) noexcept{ return *this *= rhs.inverse(); }
    constexpr modint operator++(int) noexcept{
        modint ret(*this);
        if((++value) >= mod) value -= mod;
        return ret;
    }
    constexpr modint operator--(int) noexcept{
        modint ret(*this);
        if((value += mod - 1) >= mod) value -= mod;
        return ret;
    }
    constexpr modint &operator++() noexcept{ return *this += 1; }
    constexpr modint &operator--() noexcept{ return *this -= 1; }
    friend std::ostream &operator<<(std::ostream &os, const modint<mod> &x){ return os << x.value; }
    friend std::istream &operator>>(std::istream &is, modint<mod> &x){
        int64_t i;
        is >> i;
        x = modint<mod>(i);
        return is;
    }
    friend constexpr modint<mod> pow(const modint<mod> &x, uint64_t y){
        modint<mod> ret{1}, m{x};
        while(y > 0){
            if(y & 1) ret *= m;
            m *= m;
            y >>= 1;
        }
        return ret;
    }
};

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    
    int n, m;
    cin >> n >> m;
    static int64_t x[100000], y[100000];
    for(int i=0;i<n;++i) cin >> x[i];
    for(int i=0;i<m;++i) cin >> y[i];
    
    modint<mod> xx = 0, yy = 0;
    for(int i=0;i<n;++i) xx += x[i] * (2*i+1-n);
    for(int i=0;i<m;++i) yy += y[i] * (2*i+1-m);
    cout << xx*yy << endl;
    return 0;
}