Problem:
Score : 600 points

Problem Statement

Consider the following arithmetic progression with n terms:

x, x + d, x + 2d, \ldots, x + (n-1)d

What is the product of all terms in this sequence?
Compute the answer modulo 1\ 000\ 003.

You are given Q queries of this form.
In the i-th query, compute the answer in case x = x_i, d = d_i, n = n_i.

Constraints

1 \leq Q \leq 10^5

0 \leq x_i, d_i \leq 1\ 000\ 002

1 \leq n_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

Q
x_1 d_1 n_1
:
x_Q d_Q n_Q

Output

Print Q lines.

In the i-th line, print the answer for the i-th query.

Sample Input 1

2
7 2 4
12345 67890 2019

Sample Output 1

9009
916936

For the first query, the answer is 7 \times 9 \times 11 \times 13 = 9009.
Don't forget to compute the answer modulo 1\ 000\ 003.

Solution in Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) {

    val q = readLine()!!.toInt()
    val tsl = (1..q).map { readLine()!!.split(" ").map { it.toLong() }.toTypedArray() }
    val nd = 1000003L

    tsl.forEach {
        val a0 = it[0] % nd
        val d = it[1] % nd
        val ni = it[2]

        var ans = 1L

        for(n in 1..ni){
            val r = ((a0 + ((n - 1) % nd) * d) % nd).toInt()
            ans *= if(r == 0) 1 else r

            if(ans > nd)ans %= nd
        }
        println(ans)
    }
}