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 (
    "fmt"
)

func main() {
    var n, m int 
    fmt.Scan(&n, &m) 
    x := make([]int, n)
    y := make([]int, m)
    for i := 0; i < n; i++ {
        fmt.Scan(&x[i])
    }   
    for i := 0; i < m; i++ {
        fmt.Scan(&y[i])
    }   

    const mod = 1000000007
    var yoko, tate int 
    for i := 0; i < n; i++ { // 横辺の長さ
        yoko += (x[i] * i) % mod 
        yoko = (yoko + mod - (x[i] * (n - 1 - i))) % mod 
    }   
    for i := 0; i < m; i++ { // 縦辺の長さ
        tate += (y[i] * i) % mod 
        tate = (tate + mod - (y[i] * (m - 1 - i))) % mod 
    }   
    res := (yoko * tate) % mod 
    if res < 0 { 
        res += mod 
    }   
    fmt.Println(res)
}