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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int main()
{
    int Q;
    cin >> Q;

    int x[Q], d[Q], n[Q];
    for (int i = 0; i < Q; i++)
    {
        cin >> x[i] >> d[i] >> n[i];
    }

    long int multi[Q];
    int mod = 1000003;

    for (int j = 0; j < Q; j++)
    {
        multi[j] = 1;
        for (int i = 0; i < n[j]; i++)
        {
            multi[j] *= (x[j] + (long int)i * d[j]) % mod;
            multi[j] = multi[j] % mod;
        }
    }

    for (int i = 0; i < Q; i++)
    {
        cout << multi[i] << endl;
    }

    return 0;
}