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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import *
mod=10**6+3
fac=[0 for i in range(mod)]
fac[0]=1
for i in range(0,len(fac)-1):
    fac[i+1]=(fac[i]*(i+1))%mod
fac[0]=0
Q=int(input())
for q in range(Q):
    x,d,n=map(int,input().split())
    D=pow(d,mod-2,mod)
    a,b=(x-1)*D%mod,(x+(n-1)%mod*d)*D%mod
    #print(a,b)
    if a<b:
        if 1:
            value=fac[b]*pow(fac[a-1],mod-2,mod)*pow(d,n,mod)
        #else:
        #    value=fac[b]*pow(d,n,mod)
        print(value%mod)
    else:
        print(0)