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: Accepted)

MOD = 1000003

def mypow(a,m)
#	return a**m % MOD if m < 4
	c ,res = a, 1
	while(m>0);res = res * c % MOD if m.odd?;c, m = c * c % MOD, m >> 1;end
	return res
end

def modinv(a) mypow(a, MOD-2) end
	
r = 1 ;fac = 1.upto(MOD).map { |x| r = r * x % MOD }.unshift(1)
finv = []; finv[MOD-1] = MOD - 1;
(MOD-2).downto(0) { |i| finv[i] = finv[i+1] * (i+1) % MOD}

gets
$<.read.split.map(&:to_i).each_slice(3) do |x,d,n|
	if d.zero?
		p mypow(x,n)
	elsif MOD <= n - 1 + a = modinv(d) * x % MOD or x.zero? 
		p 0
	else
		p fac[a+n-1] * finv[a] % MOD * x % MOD * mypow(d,n-1) % MOD
	end
end