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: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main {
	static final long MOD = 1000000000 + 7;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		long[] x = sc.nextLongArray(n);
		long[] y = sc.nextLongArray(m);
		Arrays.sort(x);
		Arrays.sort(y);
		long xmax = x[x.length - 1] - x[0];
		long ymax = y[y.length - 1] - y[0];
		long sum = xmax * ymax * ((x.length - 1) * (y.length - 1));
		System.out.println(String.valueOf(sum));
	}

	static class Scanner {
		private InputStream in;
		private final byte[] buf = new byte[1024];
		private int cur = 0;
		private int len = 0;

		Scanner (InputStream in) {
			this.in = in;
		}

		private int read() {
			if (cur >= len) {
				cur = 0;
				try {
					len = in.read(buf);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (len < 0) {
					return -1;
				}
			}
			return (int)buf[cur++];
		}

		public String next() {
			int c = read();
			if (c == -1) {
				throw new NoSuchElementException();
			}
			while (c < 33 || 126 < c) {
				c = read();
			}
			StringBuilder sb = new StringBuilder();
			while (33 <= c && c <= 126) {
				sb.appendCodePoint(c);
				c = read();
			}
			return sb.toString();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		public long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++) {
				array[i] = nextLong();
			}
			return array;
		}
	}
}