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

#include <stdio.h>

int main(void)
{
  int q;
  scanf("%d", &q);

  int a[q*3];
  int i,j,x,d,n;
  unsigned long long ans;
  for(i=0; i<q; i++){
    scanf("%d %d %d", &a[i*3],&a[i*3+1],&a[i*3+2]);
  }
  for(i=0; i<q; i++){
    ans = 1;
    for(j=0; j<=a[i*3+2]-1;j++){
      ans = (ans *(a[i*3] + j * a[i*3+1])) % 1000003;
    }
    printf("%llu\n", ans);
  }
    
  
  return 0;
}