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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
 
public class Main {
	InputStream is;
 
	int __t__ = 1;
	int __f__ = 0;
	int __FILE_DEBUG_FLAG__ = __f__;
	String __DEBUG_FILE_NAME__ = "src/B3";
 
	FastScanner in;
	PrintWriter out;
	
	long MOD = 1000000007;
	long sum(int[] a) {
		long cur = a.length - 1;
		long step = a.length - 3;
		long res = 0;
		for (int i = 0; i < a.length - 1; i++) {
			long diff = (a[i+1] - a[i]) % MOD;
			res = (res + (cur * diff) % MOD) % MOD;
			cur += step;
			step -= 2;
		}
		return res;
	}
	
	public void solve() {
		int n = in.nextInt();
		int m = in.nextInt();
		int[] a = in.nextIntArray(n);
		int[] b = in.nextIntArray(m);
		
		long x = sum(a);
		long y = sum(b);
		System.out.println((x * y) % MOD);
	}
	
	public void run() {
		if (__FILE_DEBUG_FLAG__ == __t__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				// TODO 自動生成された catch ブロック
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);
 
		solve();
	}
 
	public static void main(String[] args) {
		new Main().run();
	}
 
	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");
 
		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}
 
		System.out.println("----------------------------");
		System.out.println();
	}
 
	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}
 
	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
 
		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));
 
		}
 
		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();
 
			return array;
		}
 
		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();
 
			return array;
		}
 
		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();
 
			return array;
		}
 
		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}
 
		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();
 
			return array;
		}
 
		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}