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# (Mono 4.6.2.0) (judge verdict: Accepted)

#region using
using System;
using System.Collections.Generic;
using System.Linq;
using IEnumerable = System.Collections.IEnumerable;
using IEnumerator = System.Collections.IEnumerator;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;
#endregion

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Long;
            var M = consoleReader.Long;
            var xs = consoleReader.Split.Long;
            var ys = consoleReader.Split.Long;

            var yokos = new long[N - 1];
            for (int i = 0; i < N - 1; i++)
                yokos[i] = xs[i + 1] - xs[i];
            var tates = new long[M - 1];
            for (int i = 0; i < M - 1; i++)
                tates[i] = ys[i + 1] - ys[i];
            Mod sum = 0;
            Mod yoko = 0;
            for (int i = 0; i < yokos.Length; i++)
                yoko += (Mod)(i + 1) * (yokos.Length - i) * yokos[i];
            for (int i = 0; i < tates.Length; i++)
                sum += yoko * (i + 1) * (tates.Length - i) * tates[i];
            return sum;
        }
        struct Mod : IEquatable<Mod>
        {
            public const long mod = 1000000007;
            public readonly long val;
            public Mod(long val) { this.val = val; }
            public override bool Equals(object obj) => (obj is Mod) ? this == ((Mod)obj) : false;
            public bool Equals(Mod obj) => this == obj;
            public override int GetHashCode() => val.GetHashCode();
            public override string ToString() => val.ToString();
            public static implicit operator Mod(long x) => new Mod(x);
            public static Mod operator +(Mod x, Mod y) => (x.val + y.val) % mod;
            public static Mod operator -(Mod x, Mod y) => x.val >= y.val ? (x.val - y.val) % mod : (x.val - y.val) % mod + mod;
            public static Mod operator *(Mod x, Mod y) => (x.val * y.val) % mod;
            public static Mod operator /(Mod x, Mod y) => x * y.Inverse();
            public static bool operator ==(Mod x, Mod y) => x.val == y.val;
            public static bool operator !=(Mod x, Mod y) => x.val != y.val;
            public Mod Inverse()
            {
                long a = val, b = mod, u = 1, v = 0;
                while (b > 0)
                {
                    long t = a / b;
                    var b2 = a - t * b;
                    a = b; b = b2;
                    var v2 = u - t * v;
                    u = v; v = v2;
                }
                u %= mod;
                if (u < 0) u += mod;
                return u;
            }
            public static Mod Pow(Mod x, int y)
            {
                Mod res = 1;
                for (; y > 0; y >>= 1)
                {
                    if ((y & 1) == 1) res *= x;
                    x *= x;
                }
                return res;
            }

            public static Factor CreateFactor(int max) => new Factor(max);
            public class Factor
            {
                private readonly Mod[] fac, finv;
                public Factor(int max)
                {
                    ++max;
                    var inv = new Mod[max];
                    fac = new Mod[max]; finv = new Mod[max];
                    fac[0] = fac[1] = 1;
                    finv[0] = finv[1] = 1;
                    inv[1] = 1;
                    for (int i = 2; i < max; i++)
                    {
                        fac[i] = fac[i - 1] * i;
                        inv[i] = mod - inv[mod % i].val * (mod / i) % mod;
                        finv[i] = finv[i - 1] * inv[i];
                    }
                }

                // 二項係数計算
                public Mod Combine(int n, int k)
                {
                    if (n < k) return 0;
                    if (n < 0 || k < 0) return 0;
                    return fac[n] * finv[k] * finv[n - k];
                }

                public Mod Factorial(int n) => fac[n];
                public Mod FactorialInvers(int n) => finv[n];
            }
        }

        #region いつもの
#pragma warning disable
        private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
    static class Ext
    {
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public IEnumerable<string> String => this.Select(cr => cr.String); public IEnumerable<int> Int => this.Select(cr => cr.Int); public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1); public IEnumerable<long> Long => this.Select(cr => cr.Long); public IEnumerable<double> Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    #endregion
}