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: Runtime Error)

#include <iostream>
using namespace std;

typedef long long ll;
const int MOD = 1000003;

ll func(int x, int d, int n) {
  if(n == 1) return x;
  return ((x + (n-1)*d)%MOD * func(x, d, n-1)%MOD);
}

signed main() {
  int x, d, n;
  int q; cin >> q;
  for(int i = 0; i < q; i++) {
    cin >> x >> d >> n;
    cout << func(x, d, n)%MOD << endl;
  }
}