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.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		const long MOD = 1000000007;
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			int m = cin.Int();
			long[] xs = cin.ArrayLong(n);
			long[] ys = cin.ArrayLong(m);

			long x = 0;
			for (int i = 1; i < n; i++) {
				long tempX = (xs[i] - xs[i - 1]) % MOD;
				long r = n - i - 1;
				long l = i - 1;

				long temp = tempX;
				temp = (temp + ((tempX * r) % MOD)) % MOD;
				temp = (temp + ((tempX * l) % MOD)) % MOD;
				long rl = (r * l) % MOD;
				temp = (temp + ((tempX * rl) % MOD)) % MOD;

				x = (x + temp) % MOD;
			}

			long y = 0;
			for (int i = 1; i < m; i++) {
				long tempY = (ys[i] - ys[i - 1]) % MOD;
				long t = m - i - 1;
				long b = i - 1;

				long temp = tempY;
				temp = (temp + ((tempY * t) % MOD)) % MOD;
				temp = (temp + ((tempY * b) % MOD)) % MOD;
				long tb = (t * b) % MOD;
				temp = (temp + ((tempY * tb) % MOD)) % MOD;

				y = (y + temp) % MOD;
			}

			long ans = (x * y) % MOD;

			Console.WriteLine(ans);
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private string[] buf_;
		private int index_;
		Func<string> reader_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}