#include<iostream>
#include<vector>
#include<map>
#include<set>
#include<algorithm>
#include<numeric>
#include<limits>
#include<bitset>
#include<functional>
#include<type_traits>
#include<queue>
#include<stack>
#include<array>

namespace lib
{
	template<std::uint64_t Mod>struct modnum;
	template<class T>constexpr T pow(T base, std::size_t p)
	{
		if (p == 0)
		{
			return T(1);
		}
		else if (p == 1)
		{
			return base;
		}
		else if (p == 2)
		{
			return base*base;
		}
		else if (p % 2 == 0)
		{
			return pow(pow(base, p / 2), 2);
		}
		else
		{
			return pow(pow(base, p / 2), 2)*base;
		}
	}
	template<std::uint64_t Mod>constexpr auto inverse(modnum<Mod> const&);

	template<std::uint64_t Mod>struct modnum
	{
		static constexpr auto mod = Mod;
		std::uint64_t val;
		modnum() = default;
		constexpr modnum(std::uint64_t v) :val(v%Mod)
		{

		}

		constexpr modnum& operator+=(modnum const& v)
		{
			val += v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator-=(modnum const& v)
		{
			val += mod - v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator*=(modnum const& v)
		{
			val *= v.val;
			val %= mod;
			return *this;
		}
		constexpr modnum& operator/=(modnum const& v)
		{
			return operator*=(inverse(v));
		}
	};
	template<std::uint64_t Mod>constexpr auto operator+(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs += rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator-(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs -= rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator*(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs *= rhs;
	}
	template<std::uint64_t Mod>constexpr auto operator/(modnum<Mod> lhs, modnum<Mod>const& rhs)
	{
		return lhs /= rhs;
	}

	template<std::uint64_t Mod>constexpr auto inverse(modnum<Mod>const& base)
	{
		return pow(base, Mod - 2);
	}

	template<class T>constexpr auto clamp(T v)
	{
		return std::max(v, T());
	}
	template<class T>void sort(std::vector<T>& vec)
	{
		std::sort(vec.begin(), vec.end());
	}

	template<class T>auto lower_bound(std::vector<T>const& vec, T v)
	{
		return std::distance(vec.begin(), std::lower_bound(vec.begin(), vec.end(), v));
	}
	template<class T>auto upper_bound(std::vector<T>const& vec, T v)
	{
		return std::distance(vec.begin(), std::upper_bound(vec.begin(), vec.end(), v));
	}


	template<class Tag>struct dmod
	{
		std::uint64_t val;
		static std::uint64_t mod;
		dmod(std::uint64_t v = 0) :val(v%mod)
		{

		}
		dmod& operator+=(dmod const& rhs)
		{
			val += rhs.val;
			val %= mod;
			return *this;
		}
		dmod& operator-=(dmod const& rhs)
		{
			val += mod - rhs.val;
			val %= mod;
			return *this;
		}
		dmod& operator*=(dmod const& rhs)
		{
			val *= rhs.val;
			val %= mod;
			return *this;
		}
	};
	template<class Tag>dmod<Tag> operator+(dmod<Tag> lhs, dmod<Tag> const& rhs)
	{
		return lhs += rhs;
	}
	template<class Tag>dmod<Tag> operator-(dmod<Tag> lhs, dmod<Tag> const& rhs)
	{
		return lhs -= rhs;
	}
	template<class Tag>dmod<Tag> operator*(dmod<Tag> lhs, dmod<Tag> const& rhs)
	{
		return lhs *= rhs;
	}
	template<class Tag>std::uint64_t dmod<Tag>::mod;

	struct scope_exit
	{
		std::function<void(void)> func;
		scope_exit(std::function<void(void)> f) :func(f)
		{

		}
		~scope_exit()
		{
			func();
		}
	};

	template<int val>using int_tag = std::integral_constant<int, val>;
}

void Main();
int main()	
{
	std::cin.tie(nullptr);
	std::cin.sync_with_stdio(false);
	Main();
}

int count(int val, int prime)
{
	int ret = 0;
	while (val%prime == 0)
	{
		++ret;
		val /= prime;
	}
	return ret;
}

void Main()
{
	int Q;
	std::cin >> Q;
	int primes[] = { 2,3,5,7,11,13,17,19,23,29,31 };
	std::array<std::array<int, 64>, 11> counter;
	for (int i = 0; i < Q; ++i)
	{
		std::uint64_t s, n, k, b;
		std::cin >> s >> n >> k >> b;
		for (auto& v : counter)
		{
			for (auto& c : v)
			{
				c = 0;
			}
		}
		for (int i = 0; i < 11; ++i)
		{
			++counter[i][count(s, primes[i])];
		}
		for (int i = 0; i < n; ++i)
		{
			s = (s*s + s * 12345) % 100000009 + 1;
			for (int x = 0; x < 11; ++x)
			{
				++counter[x][count(s, primes[x])];
			}
		}
		int min = std::numeric_limits<int>::max();
		for (int i = 0; i < 11; ++i)
		{
			auto c = count(b, primes[i]);
			if (c == 0)
			{
				continue;
			}
			int count = 0;
			int rest = k;
			for (int j = 0; j < 64; ++j)
			{
				if (counter[i][j] >= rest)
				{
					count += j*rest;
					break;
				}
				else
				{
					count += counter[i][j] * j;
					rest -= counter[i][j];
				}
			}
			min = std::min(min, count / c);
		}
		std::cout << min << std::endl;
	}
}