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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

func main() {
	n := nextInt()
	m := nextInt()
	var X, Y int
	for i := 0; i < n; i++ {
		x := nextInt()
		X += i*x - (n-(i+1))*x
	}
	for i := 0; i < m; i++ {
		y := nextInt()
		Y += i*y - (m-(i+1))*y
	}

	p := int(math.Pow10(9)) + 7
	fmt.Println((X % p) * (Y % p) % p)
}

// Input. ----------

var sc = bufio.NewScanner(os.Stdin)

func init() {
	sc.Buffer([]byte{}, math.MaxInt64)
	sc.Split(bufio.ScanWords)
}

func nextInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}

	return i
}

func nextString() string {
	sc.Scan()
	if err := sc.Err(); err != nil {
		panic(err)
	}

	return sc.Text()
}

// ---------- Input.

// Util. ----------

func min(x, y int) int {
	return int(math.Min(float64(x), float64(y)))
}

func max(x, y int) int {
	return int(math.Max(float64(x), float64(y)))
}

// ---------- Util.