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 C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)


#if 1
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <stack>
#include <array>
#include <deque>
#include <algorithm>
#include <utility>
#include <cstdint>
#include <functional>
#include <iomanip>
#include <numeric>
#include <assert.h>
#include <bitset>
#include <list>
#include <cmath>

auto & in = std::cin;
auto& out = std::cout;
#define all_range(C) std::begin(C), std::end(C)
const double PI = 3.141592653589793238462643383279502884197169399375105820974944;

template<typename Arithmetic, typename Integral>
std::enable_if_t< std::is_unsigned<Integral>::value, Arithmetic>
ipow(Arithmetic bace, Integral n)
{
	//繰り返し二条法
	auto res = (Arithmetic)(1);
	while (n > 0) {
		if (n & 1) res *= bace;
		bace *= bace;
		n >>= 1;
	}
	return res;
}
constexpr bool is_prime(uint32_t N)
{
	if (N <= 1) {
		return false;
	}
	for (size_t i = 2; i * i <= N; ++i)
	{
		if (N % i == 0) {
			return false;
		}
	}
	return true;
}
template <uint64_t MOD> class mint_base;
//mint_base_base型用の累乗関数
template <uint64_t MOD> constexpr mint_base<MOD> m_pow(mint_base<MOD> x, uint64_t n)noexcept;
//mod計算を自動で行う整数テンプレートクラス
template <uint64_t MOD_ = 1000003>
class mint_base
{
public:
	static constexpr auto MOD = MOD_;
	static_assert(!(MOD <= 2), "MOD cannot be below 2.");
	static_assert(MOD <= (0xFFFFFFFFFFFFFFFF / 2), "MOD is too big");//加算してオーバーフローしない
	static_assert(MOD <= 0xFFFFFFFF, "MOD is too big");//乗算してオーバーフローしない
	constexpr mint_base<MOD> operator+(const mint_base<MOD>& other)const noexcept
	{
		auto v = *this;
		return v += other;
	}
	constexpr mint_base<MOD> operator-(const mint_base<MOD>& other)const noexcept
	{
		auto v = *this;
		return v -= other;
	}
	constexpr mint_base<MOD> operator*(const mint_base<MOD>& other)const noexcept
	{
		auto v = *this;
		return v *= other;
	}
	constexpr auto operator/(const mint_base<MOD>& other)const noexcept
	{
		auto v = *this;
		return v /= other;
	}
	constexpr mint_base<MOD>& operator+=(const mint_base<MOD>& other) noexcept
	{
		a += other.a;
		if (MOD <= a) { a -= MOD; };
		return *this;
	}
	constexpr mint_base<MOD>& operator-=(const mint_base<MOD>& other) noexcept
	{
		if (a >= other.a) {
			a -= other.a;
		}
		else {
			a = (a + MOD) - other.a;
		}
		return *this;
	}
	constexpr mint_base<MOD>& operator*=(const mint_base<MOD>& other) noexcept
	{
#if 1
		a *= other.a;
		a %= MOD;
#else
		//MOD <= (MAXUINT64 / 2)条件下
		uint64_t b = other.a, v = 0;
		while (b > 0) {
			if (b & 1) {
				v += a;
				if (v >= MOD)v -= MOD;
			}
			a += a;
			if (MOD <= a)a -= MOD;
			b >>= 1;
		}
		a = v;
#endif
		return *this;
	}
	constexpr mint_base<MOD>& operator/=(const mint_base<MOD>& other) noexcept
	{
		return *this *= ~other;
	}
	constexpr mint_base<MOD> operator+()const noexcept { return *this; }
	constexpr mint_base<MOD> operator-()const noexcept
	{
		return{ MOD - a, mod_value_tag{} };
	}
	constexpr mint_base<MOD>& operator++() noexcept
	{
		if (MOD <= ++a) { a = 0; };
		return *this;
	}
	constexpr mint_base<MOD>& operator--() noexcept
	{
		if (a <= 0) { a = MOD; };
		--a;
		return *this;
	}
	constexpr mint_base<MOD> operator++(int) noexcept
	{
		auto tmp = *this;
		++* this;
		return tmp;
	}
	constexpr mint_base<MOD> operator--(int) noexcept
	{
		auto tmp = *this;
		--* this;
		return tmp;
	}
	constexpr mint_base<MOD> operator~()const noexcept
	{
		return ipow(*this, e_phi - 1);
	}
	constexpr mint_base<MOD>& operator=(const mint_base<MOD>& other) noexcept
	{
		a = other.a;
		return *this;
	}
	constexpr explicit operator uint64_t()const noexcept
	{
		return a;
	}
	constexpr explicit operator unsigned()const noexcept
	{
		return (unsigned)a;
	}
	static constexpr uint64_t getmod() noexcept
	{
		return MOD;
	}
	constexpr mint_base(uint64_t a_) noexcept :a(a_% MOD) {}
	constexpr mint_base()noexcept : a(0) {}
	struct mod_value_tag {};
	constexpr mint_base(uint64_t a_, mod_value_tag) :a(a_) {}
private:
	static constexpr uint64_t get_e_phi()noexcept {
		//オイラー値の導出
		uint64_t temp = MOD;
		uint64_t m_ = MOD;
		for (uint64_t i = 2; i * i <= m_; ++i)
		{
			if (m_ % i == 0)
			{
				temp = temp / i * (i - 1);
				for (; m_ % i == 0; m_ /= i);
			}
		}
		if (m_ != 1)temp = temp / m_ * (m_ - 1);
		return temp;
	}
	static constexpr uint64_t e_phi = get_e_phi();//オイラー値
	uint64_t a;
};
//mint_base型用の累乗関数
template<uint64_t MOD>constexpr mint_base<MOD> m_pow(mint_base<MOD> x, uint64_t n)noexcept
{
	mint_base<MOD> res = 1;
	while (n > 0)
	{
		if (n & 1)res *= x;
		x *= x;
		n >>= 1;
	}
	return res;
}
//mint_baseの階乗計算
//O(x)時間が必要のため、fact_set関数を推奨する。
template<uint64_t MOD>constexpr mint_base<MOD> fact(mint_base<MOD> x)noexcept
{
	mint_base<MOD> res(1);
	for (uint64_t i = 1; i <= (uint64_t)x; ++i)
	{
		res *= i;
	}
	return res;
}
//mint_baseの階乗計算
//0からxまでの階乗を返す
//O(x)時間が必要
template<uint64_t MOD>std::vector<mint_base<MOD>> fact_set(mint_base<MOD> x = mint_base<MOD>(-1))
{
	mint_base<MOD> res(1);
	std::vector<mint_base<MOD>> set((uint64_t)(x)+1);
	set[0] = 1;
	for (uint64_t i = 1; i <= (uint64_t)x; ++i)
	{
		res *= i;
		set[i] = res;
	}
	return res;
}
//mint_base型のstreamへの出力
template<uint64_t MOD> std::ostream& operator<<(std::ostream& os, mint_base<MOD> i)
{
	os << (uint64_t)i;
	return os;
}
//mint_base型のstreamからの入力
template<uint64_t MOD> std::istream& operator >> (std::istream& is, mint_base<MOD>& i)
{
	uint64_t tmp;
	is >> tmp;
	i = tmp;
	return is;
}
typedef mint_base<1000003> mint;
namespace mint_literal {
	constexpr mint operator""_mi(unsigned long long x)noexcept {
		return mint(x);
	}
}
using namespace mint_literal;
//mint_baseの階乗計算
//0からxまでの階乗を返す
//O(N)
template<int32_t X, uint64_t MOD = mint::MOD>
/*constexpr*/ std::array<mint_base<MOD>, X + 1> fact_set_c()
{
	mint_base<MOD> res(1);
	std::array<mint_base<MOD>, X + 1> set;
	set[0] = 1;
	for (int32_t i = 1; i <= X; ++i)
	{
		res *= i;
		set[i] = res;
	}
	return set;
}



int32_t Q;

int main()
{
	static const auto fact_v = fact_set_c<mint::MOD + 3>();
	static const auto fact_div_v = [&]() {
		auto tmp = fact_v;
		for (auto& i : tmp) { i = ~i; }
		return tmp;
	}();

	using std::endl;
	in.sync_with_stdio(false);
	out.sync_with_stdio(false);
	in.tie(nullptr);
	out.tie(nullptr);

	in >> Q;
	while (Q--)
	{
		mint a, b;
		int64_t n;
		in >> a >> b >> n;
		if ((n) >= 1000003) {
			out << 0 << endl;
			continue;
		}


		mint ddd = a / b;
		uint64_t eee = (uint64_t)(ddd + n-1);
		mint res = fact_v[eee];
		if (n <= eee) {
			res *= fact_div_v[eee - n];
		}
		else {
			res *= 0;// fact_v[1000002] * fact_div_v[1000002 - (n - eee)];
		}

		out << res * m_pow(b, uint64_t(n)) << endl;
	}

	return 0;
}
#endif