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>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#define mod 1000003
int main()
{
    long long int T,i,x,d,n;
    scanf("%lld",&T);
    for(i=0;i<T;i++)
    {
        scanf("%lld %lld %lld",&x,&d,&n);
        x%=mod;
        d%=mod;
        n%=mod;
        long long int res=1;
        long long int j=0;
        while(j<=n-1)
        {
            res=res*((x+j*d)%mod);
            res%=mod;
            j++;
        }
        printf("%lld\n",res);
    }
    return 0;
}