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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::io::Read;
use std::io::{stdout, BufWriter, Write};
 
fn main() {
    let mut buf = String::new();
    
    let out = stdout();
    let mut out = BufWriter::new(out.lock());
 
    // 標準入力から全部bufに読み込む
    std::io::stdin().read_to_string(&mut buf).unwrap();
 
    // 読み込んだStringを空白で分解する
    let mut iter = buf.split_whitespace();
 
    /*
    let n: u32 = iter.next().unwrap().parse().unwrap();
    let a: i64 = iter.next().unwrap().parse().unwrap();
    let b: i64 = iter.next().unwrap().parse().unwrap();
    let c: i64 = iter.next().unwrap().parse().unwrap();
    */
    
    let q: i64 = iter.next().unwrap().parse().unwrap();
    
    for i in 0..q {
        let x: i64 = iter.next().unwrap().parse().unwrap();
        let d: i64 = iter.next().unwrap().parse().unwrap();
        let n: i64 = iter.next().unwrap().parse().unwrap();
        
        let mut sum = x % 1000003;
        for i in 1..n {
            sum *= (x + i*d);
            sum %= 1000003;
        }
        println!("{:?}",sum); 
    }    
}