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)

    using System;
    using System.Linq;
    using System.Collections.Generic;
    using Debug = System.Diagnostics.Debug;
    using StringBuilder = System.Text.StringBuilder;
    using Number = ModInteger;
    using System.Numerics;
    namespace Program
    {
        public class Solver
        {
            public void Solve()
            {
                var n = sc.Integer();
                var m = sc.Integer();
                var a = sc.Integer(n);
                var b = sc.Integer(m);
                IO.Printer.Out.WriteLine(f(a) * f(b));
            }
            ModInteger f(int[] a)
            {
                var n = a.Length;
                ModInteger ret = 0;
                var d = new ModInteger[n - 1];
                for (int i = 0; i < n - 1; i++)
                    d[i] = a[i + 1] - a[i];
                for (int i = 0; i < n - 1; i++)
                {
                    var l = i + 1;
                    var r = n - l;
                    ret += d[i] * l * r;
                }
                return ret;
            }
            public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
            static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
            static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
        }
    }

    #region main
    static class Ex
    {
        static public string AsString(this IEnumerable<char> ie) { return new string(System.Linq.Enumerable.ToArray(ie)); }
        static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
        static public void Main()
        {
            var solver = new Program.Solver();
            solver.Solve();
            Program.IO.Printer.Out.Flush();
        }
    }
    #endregion
    #region Ex
    namespace Program.IO
    {
        using System.IO;
        using System.Text;
        using System.Globalization;
        public class Printer: StreamWriter
        {
            static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; }
            public static Printer Out { get; set; }
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
            public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
            public void Write<T>(string format, T[] source) { base.Write(format, source.OfType<object>().ToArray()); }
            public void WriteLine<T>(string format, T[] source) { base.WriteLine(format, source.OfType<object>().ToArray()); }
        }
        public class StreamScanner
        {
            public StreamScanner(Stream stream) { str = stream; }
            public readonly Stream str;
            private readonly byte[] buf = new byte[1024];
            private int len, ptr;
            public bool isEof = false;
            public bool IsEndOfStream { get { return isEof; } }
            private byte read()
            {
                if (isEof) return 0;
                if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
                return buf[ptr++];
            }
            public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

            public string Scan()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                    sb.Append(b);
                return sb.ToString();
            }
            public string ScanLine()
            {
                var sb = new StringBuilder();
                for (var b = Char(); b != '\n'; b = (char)read())
                    if (b == 0) break;
                    else if (b != '\r') sb.Append(b);
                return sb.ToString();
            }
            public long Long()
            {
                if (isEof) return long.MinValue;
                long ret = 0; byte b = 0; var ng = false;
                do b = read();
                while (b != 0 && b != '-' && (b < '0' || '9' < b));
                if (b == 0) return long.MinValue;
                if (b == '-') { ng = true; b = read(); }
                for (; true; b = read())
                {
                    if (b < '0' || '9' < b)
                        return ng ? -ret : ret;
                    else ret = ret * 10 + b - '0';
                }
            }
            public int Integer() { return (isEof) ? int.MinValue : (int)Long(); }
            public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; }
            private T[] enumerate<T>(int n, Func<T> f)
            {
                var a = new T[n];
                for (int i = 0; i < n; ++i) a[i] = f();
                return a;
            }

            public char[] Char(int n) { return enumerate(n, Char); }
            public string[] Scan(int n) { return enumerate(n, Scan); }
            public double[] Double(int n) { return enumerate(n, Double); }
            public int[] Integer(int n) { return enumerate(n, Integer); }
            public long[] Long(int n) { return enumerate(n, Long); }
        }
    }
    #endregion
    #region ModNumber
    public partial struct ModInteger
    {
        public const long Mod = (long)1e9 + 7;
        public long num;
        public ModInteger(long n) : this() { num = n % Mod; if (num < 0) num += Mod; }
        public override string ToString() { return num.ToString(); }
        public static ModInteger operator +(ModInteger l, ModInteger r) { var n = l.num + r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; }
        public static ModInteger operator -(ModInteger l, ModInteger r) { var n = l.num + Mod - r.num; if (n >= Mod) n -= Mod; return new ModInteger() { num = n }; }
        public static ModInteger operator *(ModInteger l, ModInteger r) { return new ModInteger(l.num * r.num); }
        public static implicit operator ModInteger(long n) { return new ModInteger(n); }
        public static ModInteger Pow(ModInteger v, long k)
        {
            ModInteger ret = 1;
            var n = k;
            for (; n > 0; n >>= 1, v *= v)
            {
                if ((n & 1) == 1)
                    ret = ret * v;
            }
            return ret;
        }
    }
    #endregion