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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            int Q = int.Parse(Console.ReadLine());
            for (int j = 0; j < Q; j++)
            {
                string[] input = Console.ReadLine().Split(' ');
                int x = int.Parse(input[0]);
                int d = int.Parse(input[1]);
                long n = long.Parse(input[2]);
                decimal prod = 1;
                for (int i = 0; i < n; i++)
                {
                    prod *= (x + i * d);
                    prod %= 1000003;
                }
                Console.WriteLine((prod).ToString());
            }
        }
    }
}