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: Time Limit Exceeded)

import scala.io.StdIn._

object Main extends App {
  def m(s: String): Long = {
    val input = s.split(" ").map(_.toInt).toList
    val x = input.head
    val d = input(1)
    var res: BigDecimal = x
    for (n <- 1 until input(2)) {
      res = res * (x + (BigDecimal(d) * BigDecimal(n) % BigDecimal(1000003)))
      res %= 1000003
    }
    res.toInt
  }
  
  for (_ <- 1 to readInt())
    println(m(readLine()))
}