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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.io.StdIn._

object Main extends App {
  def m(s: String): Int = {
    val input = s.split(" ").toList
    val x = input.head.toDouble
    val d = input(1).toDouble
    val n = input(2).toInt
    val MOD = 10000003
    //------------------------
    val v = x / d
    val l = (0 until n).map(v + _).toList
    var ans = l.head
    for (i <- l.tail) {
      ans *= i
      if (ans > MOD) ans = ans % MOD
    }
    val res = ans * (math.pow(d, n) % MOD)
    res.toInt % MOD
  }

  for (_ <- 1 to readInt())
    println(m(readLine()))
}