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: Time Limit Exceeded)


package main

import "fmt"

func main() {
  var n, m int
  const q = uint64(1000000007)

  fmt.Scanf("%d %d", &n, &m)
  xs := make([]int64, n)
  ys := make([]int64, m)
  for i := 0; i < n; i++ {
    fmt.Scanf("%d", &(xs[i]))
  }
  for i := 0; i < m; i++ {
    fmt.Scanf("%d", &(ys[i]))
  }

  xsum := uint64(0)
  for i := 0; i < n-1; i++ {
    for j := i+1; j < n; j++ {
      xsum = (xsum + uint64(xs[j]-xs[i])) % q
    }
  }
  ysum := uint64(0)
  for i := 0; i < m-1; i++ {
    for j := i+1; j < m; j++ {
      ysum = (ysum + uint64(ys[j]-ys[i])) % q
    }
  }

  sum := (xsum * ysum) % q

  fmt.Println(sum)
}