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.

2
7 2 4
12345 67890 2019

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 $1\ 000\ 003$.