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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (N, M) = listOfInt()
    val X = listOfLong().map { ModInt(it) }.toTypedArray()
    val Y = listOfLong().map { ModInt(it) }.toTypedArray()
    var x = ModInt(0)
    for (n in 1 until N) {
        x += X[n] * n - X[n - 1]
        X[n] += X[n - 1]
    }
    var y = ModInt(0)
    for (m in 1 until M) {
        y += Y[m] * m - Y[m - 1]
        Y[m] += Y[m - 1]
    }
    println(x * y)
}   

fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfLong() = listOfString().map(String::toLong)

data class ModInt(private var v: Long) {
    companion object { private const val MOD = 1000000007L }
    init { this.v %= MOD }
    constructor(n: Int): this(n.toLong())
    operator fun plus(other: Int) = ModInt((this.v + other) % MOD)
    operator fun plus(other: ModInt) = ModInt((this.v + other.v) % MOD)
    operator fun minus(other: Int) = ModInt((this.v + MOD - other) % MOD)
    operator fun minus(other: ModInt) = ModInt((this.v + MOD - other.v) % MOD)
    operator fun times(other: Int) = ModInt(this.v * other % MOD)
    operator fun times(other: ModInt) = ModInt(this.v * other.v % MOD)
    operator fun div(other: ModInt) = ModInt(this.v * pow(other.v, MOD - 2) % MOD)
    private fun pow(a: Long, b: Long): Long {
        if (b == 0L) return 1L
        if (b % 2 == 0L) {
            val d = pow(a, b / 2)
            return (d * d) % MOD
        }
        return a * pow(a, b - 1) % MOD
    }
    override fun toString() = this.v.toString()
}