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: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
#include <cassert>
using namespace std;
#define MOD 1000003

long long bipow(long long n, long long m) {
    if (m == 0) return 1;
    if (m % 2 == 0) {
        n = (n * n) % MOD;
        return bipow(n, m / 2) % MOD;
    } else
        return (n * bipow(n, m - 1)) % MOD;
}

int main(){
    vector<long long> fac(MOD);
    fac[0] = 1;
    for(int i=1; i<MOD; i++)
        fac[i] = (fac[i-1] * i) % MOD;

    int Q;
    cin >> Q;
    for(int i=0; i<Q; i++){
        long long x, d, n;
        cin >> x >> d >> n;
        long long ans;
        if(d == 0) ans = bipow(x, n);
        else{
            long long y = (x * bipow(d, MOD-2)) % MOD;
            if(y == 0 || y + n - 1 >= MOD) ans = 0;
            else{
                long long tmp0 = bipow(d, n);
                long long tmp1 = fac[y+n-1];
                long long tmp2 = bipow(fac[y-1], MOD-2);
                ans = tmp0;
                ans = (ans * tmp1) % MOD;
                ans = (ans * tmp2) % MOD;
            }
        }
        cout << ans << endl;
    }
    return 0;
}