結果
| 問題 |
No.981 一般冪乗根
|
| ユーザー |
 Pachicobue
|
| 提出日時 | 2022-05-06 00:42:05 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 92 ms / 6,000 ms |
| コード長 | 31,746 bytes |
| コンパイル時間 | 3,555 ms |
| コンパイル使用メモリ | 231,988 KB |
| 最終ジャッジ日時 | 2025-01-29 02:37:33 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 44 |
ソースコード
#include <bits/stdc++.h>
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using f64 = double;
using f80 = long double;
using f128 = __float128;
constexpr i32 operator"" _i32(u64 v)
{
return v;
}
constexpr i32 operator"" _u32(u64 v)
{
return v;
}
constexpr i64 operator"" _i64(u64 v)
{
return v;
}
constexpr u64 operator"" _u64(u64 v)
{
return v;
}
constexpr f64 operator"" _f64(f80 v)
{
return v;
}
constexpr f80 operator"" _f80(f80 v)
{
return v;
}
using Istream = std::istream;
using Ostream = std::ostream;
using Str = std::string;
template<typename T>
using Lt = std::less<T>;
template<typename T>
using Gt = std::greater<T>;
template<typename T>
using IList = std::initializer_list<T>;
template<int n>
using BSet = std::bitset<n>;
template<typename T1, typename T2>
using Pair = std::pair<T1, T2>;
template<typename... Ts>
using Tup = std::tuple<Ts...>;
template<typename T, int N>
using Arr = std::array<T, N>;
template<typename... Ts>
using Deq = std::deque<Ts...>;
template<typename... Ts>
using Set = std::set<Ts...>;
template<typename... Ts>
using MSet = std::multiset<Ts...>;
template<typename... Ts>
using USet = std::unordered_set<Ts...>;
template<typename... Ts>
using UMSet = std::unordered_multiset<Ts...>;
template<typename... Ts>
using Map = std::map<Ts...>;
template<typename... Ts>
using MMap = std::multimap<Ts...>;
template<typename... Ts>
using UMap = std::unordered_map<Ts...>;
template<typename... Ts>
using UMMap = std::unordered_multimap<Ts...>;
template<typename... Ts>
using Vec = std::vector<Ts...>;
template<typename... Ts>
using Stack = std::stack<Ts...>;
template<typename... Ts>
using Queue = std::queue<Ts...>;
template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>;
using NSec = std::chrono::nanoseconds;
using USec = std::chrono::microseconds;
using MSec = std::chrono::milliseconds;
using Sec = std::chrono::seconds;
template<typename T>
constexpr T LIMMIN = std::numeric_limits<T>::min();
template<typename T>
constexpr T LIMMAX = std::numeric_limits<T>::max();
template<typename T>
constexpr T INF = (LIMMAX<T> - 1) / 2;
template<typename T>
constexpr T PI = T{3.141592653589793238462643383279502884};
template<typename T = u64>
constexpr T TEN(const int n)
{
return n == 0 ? T{1} : TEN<T>(n - 1) * T{10};
}
Ostream& operator<<(Ostream& os, i128 v)
{
bool minus = false;
if (v < 0) { minus = true, v = -v; }
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << (minus ? "-" : "") << ans;
}
Ostream& operator<<(Ostream& os, u128 v)
{
Str ans;
if (v == 0) { ans = "0"; }
while (v) {
ans.push_back('0' + v % 10), v /= 10;
}
std::reverse(ans.begin(), ans.end());
return os << ans;
}
template<typename T>
bool chmin(T& a, const T& b)
{
if (a > b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
bool chmax(T& a, const T& b)
{
if (a < b) {
a = b;
return true;
} else {
return false;
}
}
template<typename T>
constexpr T floorDiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? x / y : (x - y + 1) / y;
}
template<typename T>
constexpr T ceilDiv(T x, T y)
{
if (y < T{}) { x = -x, y = -y; }
return x >= T{} ? (x + y - 1) / y : x / y;
}
template<typename T, typename I>
constexpr T modPower(T v, I n, T mod)
{
T ans = 1 % mod;
for (; n > 0; n >>= 1, (v *= v) %= mod) {
if (n % 2 == 1) { (ans *= v) %= mod; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n)
{
T ans = 1;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T, typename I>
constexpr T power(T v, I n, const T& e)
{
T ans = e;
for (; n > 0; n >>= 1, v *= v) {
if (n % 2 == 1) { ans *= v; }
}
return ans;
}
template<typename T>
Vec<T> operator+=(Vec<T>& vs1, const Vec<T>& vs2)
{
vs1.insert(vs1.end(), vs2.begin(), vs2.end());
return vs1;
}
template<typename T>
Vec<T> operator+(const Vec<T>& vs1, const Vec<T>& vs2)
{
auto vs = vs1;
vs += vs2;
return vs;
}
template<typename Vs, typename V>
void fillAll(Vs& arr, const V& v)
{
if constexpr (std::is_convertible<V, Vs>::value) {
arr = v;
} else {
for (auto& subarr : arr) {
fillAll(subarr, v);
}
}
}
template<typename Vs>
void sortAll(Vs& vs)
{
std::sort(std::begin(vs), std::end(vs));
}
template<typename Vs, typename C>
void sortAll(Vs& vs, C comp)
{
std::sort(std::begin(vs), std::end(vs), comp);
}
template<typename Vs>
void reverseAll(Vs& vs)
{
std::reverse(std::begin(vs), std::end(vs));
}
template<typename V, typename Vs>
V sumAll(const Vs& vs)
{
if constexpr (std::is_convertible<Vs, V>::value) {
return static_cast<V>(vs);
} else {
V ans = 0;
for (const auto& v : vs) {
ans += sumAll<V>(v);
}
return ans;
}
}
template<typename Vs>
int minInd(const Vs& vs)
{
return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs>
int maxInd(const Vs& vs)
{
return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs, typename V>
int lbInd(const Vs& vs, const V& v)
{
return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
int ubInd(const Vs& vs, const V& v)
{
return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename T, typename F>
Vec<T> genVec(int n, F gen)
{
Vec<T> ans;
std::generate_n(std::back_insert_iterator(ans), n, gen);
return ans;
}
Vec<int> iotaVec(int n, int offset = 0)
{
Vec<int> ans(n);
std::iota(ans.begin(), ans.end(), offset);
return ans;
}
constexpr int popcount(const u64 v)
{
return v ? __builtin_popcountll(v) : 0;
}
constexpr int log2p1(const u64 v)
{
return v ? 64 - __builtin_clzll(v) : 0;
}
constexpr int lsbp1(const u64 v)
{
return __builtin_ffsll(v);
}
constexpr int clog(const u64 v)
{
return v ? log2p1(v - 1) : 0;
}
constexpr u64 ceil2(const u64 v)
{
const int l = clog(v);
return (l == 64) ? 0_u64 : (1_u64 << l);
}
constexpr u64 floor2(const u64 v)
{
return v ? (1_u64 << (log2p1(v) - 1)) : 0_u64;
}
constexpr bool ispow2(const u64 v)
{
return (v > 0) and ((v & (v - 1)) == 0);
}
constexpr bool btest(const u64 mask, const int ind)
{
return (mask >> ind) & 1_u64;
}
template<typename F>
struct Fix : F
{
Fix(F&& f) : F{std::forward<F>(f)} {}
template<typename... Args>
auto operator()(Args&&... args) const
{
return F::operator()(*this, std::forward<Args>(args)...);
}
};
class irange
{
private:
struct itr
{
itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {}
bool operator!=(const itr& it) const
{
return m_cnt != it.m_cnt;
}
int operator*()
{
return m_cnt;
}
itr& operator++()
{
m_cnt += m_step;
return *this;
}
i64 m_cnt, m_step;
};
i64 m_start, m_end, m_step;
public:
irange(i64 start, i64 end, i64 step = 1)
{
assert(step != 0);
const i64 d = std::abs(step);
const i64 l = (step > 0 ? start : end);
const i64 r = (step > 0 ? end : start);
int n = (r - l) / d + ((r - l) % d ? 1 : 0);
if (l >= r) { n = 0; }
m_start = start;
m_end = start + step * n;
m_step = step;
}
itr begin() const
{
return itr{m_start, m_step};
}
itr end() const
{
return itr{m_end, m_step};
}
};
irange rep(int end)
{
return irange(0, end, 1);
}
irange per(int rend)
{
return irange(rend - 1, -1, -1);
}
/**
* @ref https://prng.di.unimi.it
*/
namespace xoshiro_impl {
u64 x;
u64 next()
{
uint64_t z = (x += 0x9e3779b97f4a7c15);
z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
return z ^ (z >> 31);
}
} // namespace xoshiro_impl
class Xoshiro32
{
public:
using result_type = u32;
using T = result_type;
Xoshiro32(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (32 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 9;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 11);
return ans;
}
T s[4];
};
class Xoshiro64
{
public:
using result_type = u64;
using T = result_type;
Xoshiro64(T seed = 0)
{
xoshiro_impl::x = seed;
s[0] = xoshiro_impl::next();
s[1] = xoshiro_impl::next();
s[2] = xoshiro_impl::next();
s[3] = xoshiro_impl::next();
}
static constexpr T min()
{
return LIMMIN<T>;
}
static constexpr T max()
{
return LIMMAX<T>;
}
T operator()()
{
return next();
}
private:
static constexpr T rotl(const T x, int k)
{
return (x << k) | (x >> (64 - k));
}
T next()
{
const T ans = rotl(s[1] * 5, 7) * 9;
const T t = s[1] << 17;
s[2] ^= s[0];
s[3] ^= s[1];
s[1] ^= s[2];
s[0] ^= s[3];
s[2] ^= t;
s[3] = rotl(s[3], 45);
return ans;
}
T s[4];
};
template<typename Rng>
class RNG
{
public:
using result_type = typename Rng::result_type;
using T = result_type;
static constexpr T min()
{
return Rng::min();
}
static constexpr T max()
{
return Rng::max();
}
RNG() : RNG(std::random_device{}()) {}
RNG(T seed) : m_rng(seed) {}
T operator()()
{
return m_rng();
}
template<typename T>
T val(T min, T max)
{
return std::uniform_int_distribution<T>(min, max)(m_rng);
}
template<typename T>
Pair<T, T> pair(T min, T max)
{
return std::minmax({val<T>(min, max), val<T>(min, max)});
}
template<typename T>
Vec<T> vec(int n, T min, T max)
{
return genVec<T>(n, [&]() { return val<T>(min, max); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, T min, T max)
{
return genVec<Vec<T>>(n, [&]() { return vec(m, min, max); });
}
private:
Rng m_rng;
};
RNG<std::mt19937> rng;
RNG<std::mt19937_64> rng64;
RNG<Xoshiro32> rng_xo;
RNG<Xoshiro64> rng_xo64;
template<typename K, typename V, int LG = 20>
class IntDict
{
public:
IntDict() = default;
V& operator[](K k)
{
const auto i = index(k);
if (not m_used.test(i)) {
m_used.set(i), m_keys[i] = k;
m_vals[i] = V{};
}
return m_vals[i];
}
const V& at(K k) const
{
return m_vals[index(k)];
}
void erase(K k)
{
m_used.reset(index(k));
}
bool contains(K k) const
{
const auto i = index(k);
return m_used.test(i) and m_keys[i] == k;
}
private:
u32 index(K k) const
{
u32 i = 0;
for (i = fibHash(k); m_used.test(i) and m_keys[i] != k;
(i += 1) &= (N - 1)) {}
return i;
}
static constexpr int N = 1 << LG;
static constexpr u32 fibHash(u64 k)
{
constexpr u64 a = 11400714819323198485_u64;
return (a * k) >> (64 - LG);
}
BSet<N> m_used;
Arr<K, N> m_keys;
Arr<V, N> m_vals;
};
template<typename T>
constexpr Pair<T, T> extgcd(const T a, const T b) // [x,y] -> ax+by=gcd(a,b)
{
static_assert(std::is_signed<T>::value,
"extgcd: Only signed integer supported.");
assert(a != 0 or b != 0);
if (a >= 0 and b >= 0) {
if (a < b) {
const auto [y, x] = extgcd(b, a);
return {x, y};
}
if (b == 0) { return {1, 0}; }
const auto [x, y] = extgcd(b, a % b);
return {y, x - (a / b) * y};
} else {
auto [x, y] = extgcd(std::abs(a), std::abs(b));
if (a < 0) { x = -x; }
if (b < 0) { y = -y; }
return {x, y};
}
}
template<typename T>
constexpr T inverse(const T a, const T mod) // ax=gcd(a,M) (mod M)
{
assert(a > 0 and mod > 0);
auto [x, y] = extgcd(a, mod);
if (x <= 0) { x += mod; }
return x;
}
template<u32 mod_, u32 root_, u32 max2p_>
class modint
{
template<typename U = u32&>
static U modRef()
{
static u32 s_mod = 0;
return s_mod;
}
template<typename U = u32&>
static U rootRef()
{
static u32 s_root = 0;
return s_root;
}
template<typename U = u32&>
static U max2pRef()
{
static u32 s_max2p = 0;
return s_max2p;
}
public:
static constexpr bool isDynamic()
{
return (mod_ == 0);
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> mod()
{
return mod_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> mod()
{
return modRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> root()
{
return root_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> root()
{
return rootRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> max2p()
{
return max2p_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> max2p()
{
return max2pRef();
}
template<typename U = u32>
static void setMod(std::enable_if_t<mod_ == 0, U> m)
{
modRef() = m;
}
template<typename U = u32>
static void setRoot(std::enable_if_t<mod_ == 0, U> r)
{
rootRef() = r;
}
template<typename U = u32>
static void setMax2p(std::enable_if_t<mod_ == 0, U> m)
{
max2pRef() = m;
}
constexpr modint() : m_val{0} {}
constexpr modint(i64 v) : m_val{normll(v)} {}
constexpr void setRaw(u32 v)
{
m_val = v;
}
constexpr modint operator-() const
{
return modint{0} - (*this);
}
constexpr modint& operator+=(const modint& m)
{
m_val = norm(m_val + m.val());
return *this;
}
constexpr modint& operator-=(const modint& m)
{
m_val = norm(m_val + mod() - m.val());
return *this;
}
constexpr modint& operator*=(const modint& m)
{
m_val = normll((i64)m_val * (i64)m.val() % (i64)mod());
return *this;
}
constexpr modint& operator/=(const modint& m)
{
return *this *= m.inv();
}
constexpr modint operator+(const modint& m) const
{
auto v = *this;
return v += m;
}
constexpr modint operator-(const modint& m) const
{
auto v = *this;
return v -= m;
}
constexpr modint operator*(const modint& m) const
{
auto v = *this;
return v *= m;
}
constexpr modint operator/(const modint& m) const
{
auto v = *this;
return v /= m;
}
constexpr bool operator==(const modint& m) const
{
return m_val == m.val();
}
constexpr bool operator!=(const modint& m) const
{
return not(*this == m);
}
friend Istream& operator>>(Istream& is, modint& m)
{
i64 v;
return is >> v, m = v, is;
}
friend Ostream& operator<<(Ostream& os, const modint& m)
{
return os << m.val();
}
constexpr u32 val() const
{
return m_val;
}
template<typename I>
constexpr modint pow(I n) const
{
return power(*this, n);
}
constexpr modint inv() const
{
return pow(mod() - 2);
}
static modint sinv(u32 n)
{
static Vec<modint> is{1, 1};
for (u32 i = (u32)is.size(); i <= n; i++) {
is.push_back(-is[mod() % i] * (mod() / i));
}
return is[n];
}
static modint fact(u32 n)
{
static Vec<modint> fs{1, 1};
for (u32 i = (u32)fs.size(); i <= n; i++) {
fs.push_back(fs.back() * i);
}
return fs[n];
}
static modint ifact(u32 n)
{
static Vec<modint> ifs{1, 1};
for (u32 i = (u32)ifs.size(); i <= n; i++) {
ifs.push_back(ifs.back() * sinv(i));
}
return ifs[n];
}
static modint comb(int n, int k)
{
return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k);
}
private:
static constexpr u32 norm(u32 x)
{
return x < mod() ? x : x - mod();
}
static constexpr u32 normll(i64 x)
{
return norm(u32(x % (i64)mod() + (i64)mod()));
}
u32 m_val;
};
using modint_1000000007 = modint<1000000007, 5, 1>;
using modint_998244353 = modint<998244353, 3, 23>;
template<int id>
using modint_dynamic = modint<0, 0, id>;
template<u64 mod_, u64 root_, u64 max2p_>
class modint64
{
template<typename U = u64&>
static U modRef()
{
static u64 s_mod = 0;
return s_mod;
}
template<typename U = u64&>
static U rootRef()
{
static u64 s_root = 0;
return s_root;
}
template<typename U = u64&>
static U max2pRef()
{
static u64 s_max2p = 0;
return s_max2p;
}
public:
static constexpr bool isDynamic()
{
return (mod_ == 0);
}
template<typename U = const u64>
static constexpr std::enable_if_t<mod_ != 0, U> mod()
{
return mod_;
}
template<typename U = const u64>
static std::enable_if_t<mod_ == 0, U> mod()
{
return modRef();
}
template<typename U = const u64>
static constexpr std::enable_if_t<mod_ != 0, U> root()
{
return root_;
}
template<typename U = const u64>
static std::enable_if_t<mod_ == 0, U> root()
{
return rootRef();
}
template<typename U = const u64>
static constexpr std::enable_if_t<mod_ != 0, U> max2p()
{
return max2p_;
}
template<typename U = const u64>
static std::enable_if_t<mod_ == 0, U> max2p()
{
return max2pRef();
}
template<typename U = u64>
static void setMod(std::enable_if_t<mod_ == 0, U> m)
{
modRef() = m;
}
template<typename U = u64>
static void setRoot(std::enable_if_t<mod_ == 0, U> r)
{
rootRef() = r;
}
template<typename U = u64>
static void setMax2p(std::enable_if_t<mod_ == 0, U> m)
{
max2pRef() = m;
}
constexpr modint64() : m_val{0} {}
constexpr modint64(const i64 v) : m_val{normLL(v)} {}
constexpr void setRaw(const u64 v)
{
m_val = v;
}
constexpr modint64 operator+() const
{
return *this;
}
constexpr modint64 operator-() const
{
return modint64{0} - (*this);
}
constexpr modint64& operator+=(const modint64& m)
{
m_val = norm(m_val + m.val());
return *this;
}
constexpr modint64& operator-=(const modint64& m)
{
m_val = norm(m_val + mod() - m.val());
return *this;
}
constexpr modint64& operator*=(const modint64& m)
{
m_val = normLL((i128)m_val * (i128)m.val() % (i128)mod());
return *this;
}
constexpr modint64& operator/=(const modint64& m)
{
return *this *= m.inv();
}
constexpr modint64 operator+(const modint64& m) const
{
auto v = *this;
return v += m;
}
constexpr modint64 operator-(const modint64& m) const
{
auto v = *this;
return v -= m;
}
constexpr modint64 operator*(const modint64& m) const
{
auto v = *this;
return v *= m;
}
constexpr modint64 operator/(const modint64& m) const
{
auto v = *this;
return v /= m;
}
constexpr bool operator==(const modint64& m) const
{
return m_val == m.val();
}
constexpr bool operator!=(const modint64& m) const
{
return not(*this == m);
}
friend Istream& operator>>(Istream& is, modint64& m)
{
i64 v;
return is >> v, m = v, is;
}
friend Ostream& operator<<(Ostream& os, const modint64& m)
{
return os << m.val();
}
constexpr u64 val() const
{
return m_val;
}
template<typename I>
constexpr modint64 pow(I n) const
{
return power(*this, n);
}
constexpr modint64 inv() const
{
return pow(mod() - 2);
}
modint64 sinv() const
{
return sinv(m_val);
}
static modint64 fact(u32 n)
{
static Vec<modint64> fs{1, 1};
for (u32 i = (u32)fs.size(); i <= n; i++) {
fs.push_back(fs.back() * i);
}
return fs[n];
}
static modint64 ifact(u32 n)
{
static Vec<modint64> ifs{1, 1};
for (u32 i = (u32)ifs.size(); i <= n; i++) {
ifs.push_back(ifs.back() * sinv(i));
}
return ifs[n];
}
static modint64 perm(int n, int k)
{
return k > n or k < 0 ? modint64{0} : fact(n) * ifact(n - k);
}
static modint64 comb(int n, int k)
{
return k > n or k < 0 ? modint64{0} : fact(n) * ifact(n - k) * ifact(k);
}
private:
static constexpr u64 norm(const u64 x)
{
return x < mod() ? x : x - mod();
}
static constexpr u64 normLL(const i64 x)
{
return norm(u64((i128)x % (i128)mod() + (i128)mod()));
}
static modint64 sinv(u32 n)
{
static Vec<modint64> is{1, 1};
for (u32 i = (u32)is.size(); i <= n; i++) {
is.push_back(-is[mod() % i] * (mod() / i));
}
return is[n];
}
u64 m_val;
};
template<int id>
using modint64_dynamic = modint64<0, 0, id>;
template<typename mint>
bool millerRabin(u64 n, const Vec<u64>& as)
{
auto d = n - 1;
for (; (d & 1) == 0; d >>= 1) {}
for (const u64 a : as) {
if (n <= a) { break; }
auto s = d;
mint x = mint(a).pow(s);
while (x.val() != 1 and x.val() != n - 1 and s != n - 1) {
x *= x, s <<= 1;
}
if (x.val() != n - 1 and s % 2 == 0) { return false; }
}
return true;
}
bool isPrime(u64 n)
{
using mint = modint_dynamic<873293817>;
using mint64 = modint64_dynamic<828271328>;
if (n == 1) { return false; }
if ((n & 1) == 0) { return n == 2; }
if (n < (1ULL << 30)) {
mint::setMod(n);
return millerRabin<mint>(n, {2, 7, 61});
} else {
mint64::setMod(n);
return millerRabin<mint64>(n, {2, 325, 9375, 28178, 450775, 9780504});
}
}
template<typename mint>
u64 pollardRho(u64 n)
{
if (n % 2 == 0) { return 2; }
if (isPrime(n)) { return n; }
mint c;
auto f = [&](const mint& x) { return x * x + c; };
while (true) {
mint x, y, ys, q = 1;
y = rng64.val<u64>(0, n - 2) + 2;
c = rng64.val<u64>(0, n - 2) + 2;
u64 d = 1;
constexpr u32 dk = 128;
for (u32 r = 1; d == 1; r <<= 1) {
x = y;
for (u32 i = 0; i < r; i++) {
y = f(y);
}
for (u32 k = 0; k < r and d == 1; k += dk) {
ys = y;
for (u32 i = 0; i < dk and i < r - k; i++) {
q *= x - (y = f(y));
}
d = std::gcd((u64)q.val(), n);
}
}
if (d == n) {
do {
d = std::gcd(u64((x - (ys = f(ys))).val()), n);
} while (d == 1);
}
if (d != n) { return d; }
}
return n;
}
Map<u64, int> primeFactors(u64 n)
{
using mint = modint_dynamic<287687412>;
using mint64 = modint64_dynamic<4832432>;
Map<u64, int> ans;
Fix([&](auto dfs, u64 x) -> void {
while ((x & 1) == 0) {
x >>= 1, ans[2]++;
}
if (x == 1) { return; }
u64 p;
if (x < (1ULL << 30)) {
mint::setMod(x);
p = pollardRho<mint>(x);
} else {
mint64::setMod(x);
p = pollardRho<mint64>(x);
}
if (p == x) {
ans[p]++;
return;
}
dfs(p), dfs(x / p);
})(n);
return ans;
}
Vec<u64> divisors(const u64 n)
{
const auto fs = primeFactors(n);
Vec<u64> ds{1};
for (const auto& [p, e] : fs) {
u64 pe = p;
const u32 dn = ds.size();
for (i32 i = 0; i < e; i++, pe *= p) {
for (u32 j = 0; j < dn; j++) {
ds.push_back(ds[j] * pe);
}
}
}
return ds;
}
template<typename mint>
mint modNthRoot(mint A, i64 k)
{
const i64 P = mint::mod();
assert(P > 0);
if (A == 0) { return 0; }
if (k == 0) { return A; }
const i64 g = std::gcd(P - 1, k);
if (A.pow((P - 1) / g).val() != 1) { return 0; }
A = A.pow(inverse(k / g, (P - 1) / g));
if (g == 1) { return A; }
const auto fs = primeFactors(g);
for (const auto& [p, e] : fs) {
i64 pe = 1;
for (int i = 0; i < e; i++) {
pe *= p;
}
i64 q = P - 1, Q = 0;
while (q % p == 0) {
q /= p, Q++;
}
auto [y, z] = extgcd(-q, pe);
if (y <= 0) { y += pe, z += q; }
mint X = A.pow(z);
if ((int)Q == e) {
A = X;
continue;
}
mint Eraser = 1;
const i64 h = (P - 1) / p;
for (mint Z = 2;; Z += 1) {
if (Z.pow(h) != 1) {
Eraser = Z.pow(q);
break;
}
}
mint Error = A.pow(y * q);
mint pEraser = Eraser;
for (i64 i = 0; i < Q - 1; i++) {
pEraser = pEraser.pow(p);
}
const mint ipEraser = pEraser.inv();
IntDict<i64, i64> memo;
{
const i64 M
= std::max(1_i64, (i64)(std::sqrt(p) * std::sqrt(Q - e)));
const i64 B = std::max(1_i64, ((i64)p - 1) / M);
const mint ppEraser = pEraser.pow(B);
mint prod = 1;
for (i64 i = 0; i < p; i += B, prod *= ppEraser) {
memo[prod.val()] = i;
}
}
while (Error.val() != 1) {
i64 l = 0;
mint pError = Error;
for (i64 i = 0; i < Q; i++) {
const auto npError = pError.pow(p);
if (npError == 1) {
l = Q - (i + 1);
break;
}
pError = npError;
}
i64 c = -1;
{
mint small = pError.inv();
for (i64 j = 0;; j++, small *= ipEraser) {
if (memo.contains(small.val())) {
const i64 i = memo[small.val()];
c = i + j;
break;
}
}
}
auto pEraser2 = Eraser.pow(c);
for (i64 i = 0; i < l - e; i++) {
pEraser2 = pEraser2.pow(p);
}
X *= pEraser2, Error *= pEraser2.pow(pe);
}
A = X;
}
return A;
}
#pragma region FastIO Printer
class Printer
{
public:
Printer() {}
template<typename... Args>
int operator()(const Args&... args)
{
dump(args...);
return 0;
}
template<typename... Args>
int ln(const Args&... args)
{
dump(args...), putchar('\n');
return 0;
}
private:
template<typename T>
void dump(T v)
{
static char tmp[30];
if (v < 0) {
putchar('-');
v = -v;
}
int i = 0;
do {
tmp[i++] = v % T{10} + '0';
v /= T{10};
} while (v);
while (i) {
putchar(tmp[--i]);
}
}
void dump(bool b)
{
dump<int>(b);
}
void dump(char c)
{
putchar(c);
}
void dump(const Str& cs)
{
for (char c : cs) {
dump(c);
}
}
template<typename T>
void dump(const Vec<T>& vs)
{
for (const int i : rep(vs.size())) {
if (i) { putchar(' '); }
dump(vs[i]);
}
}
template<typename T>
void dump(const Vec<Vec<T>>& vss)
{
for (const int i : rep(vss.size())) {
if (i) { putchar('\n'); }
dump(vss[i]);
}
}
template<typename T, typename... Ts>
int dump(const T& v, const Ts&... args)
{
dump(v), putchar(' '), dump(args...);
return 0;
}
static inline void putchar(char c)
{
putchar_unlocked(c);
}
} out;
#pragma endregion
#pragma region FastIO Scanner
class Scanner
{
public:
Scanner() {}
template<typename T>
T val()
{
T ans = 0;
bool neg = false;
char c = getchar();
if (c < '0') {
neg = true;
} else {
ans = c - '0';
}
while (true) {
c = getchar();
if (c < '0') { break; }
ans = ans * T{10} + (c - '0');
}
if (neg) { ans = -ans; }
return ans;
}
template<typename T>
T val(T offset)
{
return val<T>() - offset;
}
template<typename T>
Vec<T> vec(int n)
{
return genVec<T>(n, [&]() { return val<T>(); });
}
template<typename T>
Vec<T> vec(int n, T offset)
{
return genVec<T>(n, [&]() { return val<T>(offset); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, T offset)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); });
}
template<typename... Args>
auto tup()
{
return std::tuple<Args...>{val<Args>()...};
}
template<typename... Args>
auto tup(const Args&... offsets)
{
return std::tuple<Args...>{val<Args>(offsets)...};
}
private:
static inline char getchar()
{
return getchar_unlocked();
}
} in;
template<>
char Scanner::val()
{
return Scanner::getchar();
}
template<>
Str Scanner::val()
{
Str ans;
while (true) {
const char c = Scanner::getchar();
if (c == ' ' or c == '\n' or c == EOF) { break; }
ans.push_back(c);
}
return ans;
}
// #pragma endregion
using mint = modint64_dynamic<0>;
int main()
{
const int T = in.val<int>();
for (int t : rep(T)) {
const auto [P, K, Y] = in.tup<u64, u64, u64>();
if (P == 2) {
out.ln(Y == 1 ? 1 : K == 0 ? -1 : 0);
continue;
}
mint::setMod(P);
const mint ans = modNthRoot(mint(Y), K);
if (ans.pow(K) == Y) {
out.ln(ans.val());
} else {
out.ln(-1);
}
}
return 0;
}