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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

my $q = <STDIN>;
chomp($q);
my @x=();
my @d=();
my @n=();
for (1..$q)
{
    my $p = <STDIN>;
    chomp($p);
    my ($a, $b, $c) = split / /, $p;
    push(@x,$a);
    push(@d,$b);
    push(@n,$c);
}

for my $i(0..$q-1)
{
    my $ans=1;
    for my $j (0..$n[$i]-1)
    {
	$ans = ($ans * ( $x[$i] + $j * $d[$i] )) % 1000003;
    }

    print "$ans\n";
}

1;