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)

def product(first, diff, n)
    ret = first
    (1..n-1).each do |i|
        ret = (ret * ((first + diff * i) % 1000003)) % 1000003
    end
    return ret
end


q = gets.chomp.to_i
ans = Array.new

q.times do
    input = gets.chomp.split(" ").map(&:to_i)
    ans.push(product(input[0], input[1], input[2]))
end

(0..q-1).each do |i|
    puts ans[i]
end