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 Kotlin (1.0.0) (judge verdict: Runtime Error)

import java.math.BigInteger

fun main(args: Array<String>) {
    val mod = 1000003L
    fun divWithMod(a: Long, b: Long): Long {
        return ((a % mod) * BigInteger.valueOf(b).modInverse(BigInteger.valueOf(mod)).toLong()) % mod
    }
    fun pow(a: Long, b: Long): Long {
        var bt = b
        var ret = 1L
        var at = a
        while (bt > 0) {
            if (bt and 1 == 1L) ret = ret * at % mod
            at = at * at % mod
            bt = bt shr 1
        }
        return ret
    }

    val fact = mutableListOf(0L,1L)
    (2..mod).forEach { fact.add(it * fact[it.toInt() - 1] % mod) }

    val q = readLine()!!.toInt()
    for (i in 1..q) {
        val (x, d, n) = readLine()!!.split(' ').map(String::toLong)
        if (d == 0L) {
            println(pow(d, n))
        } else {
            val powd = pow(d, n)
            val fact1 = fact[(divWithMod(x, d) + (n - 1)).toInt()]
            val fact2 = fact[(divWithMod(x, d) - 1).toInt()]
            val ans = divWithMod(powd * fact1, fact2)
            println(ans)
        }
    }
}