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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int q = sc.nextInt();
		long[] answer = new long[q];
		for (int i = 0; i<q; i++) {
			int x = sc.nextInt();
			int d = sc.nextInt();
			int n = sc.nextInt();
			answer[i] = calc(x,d,n);
		}

		for (long a : answer ) {
			System.out.println(a);
		}

	}

	static long calc(Integer x, Integer d, Integer n) {
		long result = 1;
		for (int i = 0; i < n; i++) {
			int val = (x + i * d) % 1000003;
			result = (result * val) % 1000003;
		}

		result = result % 1000003;
		return result;
	}


}