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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

M=1000003
o=->a,n{n<1?1:(n%2>0?a:1)*o[a,n/2]**2%M}
*f=1
1.upto(M){|i|f<<f[i-1]*i%M}
gets
$<.map{|s|eval'X,D,N='+s.split*?,
t=X*o[D,M-2]%M
p D<1?o[X,N]:M<t+N||t<1?0:f[t+N-1]*o[f[t-1],M-2]*o[D,N]%M}