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)

/**
    AUTHOR:JUNSH
    TIME:19/6/1
**/
#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define rev(i,a,b) for(int i=(a);i>=(b);--i)
using namespace std;
typedef long long ll;
const int mod=1e6+3;
ll fac[mod+10];
ll quick_pow(ll x,ll n){
    ll res=1;
    while(n){
        if(n&1){
            res=(res*x)%mod;
        }
        n=n>>1;
        x=(x*x)%mod;
    }
    return res;
}
ll inv(ll x){
    return quick_pow(x,mod-2);
}
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    ll x,d,n;
    fac[0]=1;
    rep(i,1,mod){
        fac[i]=(fac[i-1]*i)%mod;
    }
    ll q;
    cin>>q;
    while(q--){
        cin>>x>>d>>n;
        if(!d){
            cout<<quick_pow(x,n)<<endl;
            continue;
        }
        x=x*inv(d)%mod;
        if(x+n-1>=mod){
            cout<<"0"<<endl;
            continue;
        }
        cout<<fac[x+n-1]*inv(fac[x-1])%mod*quick_pow(d,n)%mod<<endl;
    }

}