#include 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 using Lt = std::less; template using Gt = std::greater; template using IList = std::initializer_list; template using BSet = std::bitset; template using Pair = std::pair; template using Tup = std::tuple; template using Arr = std::array; template using Deq = std::deque; template using Set = std::set; template using MSet = std::multiset; template using USet = std::unordered_set; template using UMSet = std::unordered_multiset; template using Map = std::map; template using MMap = std::multimap; template using UMap = std::unordered_map; template using UMMap = std::unordered_multimap; template using Vec = std::vector; template using Stack = std::stack; template using Queue = std::queue; template using MaxHeap = std::priority_queue; template using MinHeap = std::priority_queue, Gt>; using NSec = std::chrono::nanoseconds; using USec = std::chrono::microseconds; using MSec = std::chrono::milliseconds; using Sec = std::chrono::seconds; template constexpr T LIMMIN = std::numeric_limits::min(); template constexpr T LIMMAX = std::numeric_limits::max(); template constexpr T INF = (LIMMAX - 1) / 2; template constexpr T PI = T{3.141592653589793238462643383279502884}; template constexpr T TEN(const int n) { return n == 0 ? T{1} : TEN(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 bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } else { return false; } } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else { return false; } } template constexpr T floorDiv(T x, T y) { if (y < T{}) { x = -x, y = -y; } return x >= T{} ? x / y : (x - y + 1) / y; } template constexpr T ceilDiv(T x, T y) { if (y < T{}) { x = -x, y = -y; } return x >= T{} ? (x + y - 1) / y : x / y; } template 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 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 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 Vec& operator+=(Vec& vs1, const Vec& vs2) { vs1.insert(vs1.end(), vs2.begin(), vs2.end()); return vs1; } template Vec operator+(const Vec& vs1, const Vec& vs2) { auto vs = vs1; vs += vs2; return vs; } template void fillAll(Vs& arr, const V& v) { if constexpr (std::is_convertible::value) { arr = v; } else { for (auto& subarr : arr) { fillAll(subarr, v); } } } template void sortAll(Vs& vs) { std::sort(std::begin(vs), std::end(vs)); } template void sortAll(Vs& vs, C comp) { std::sort(std::begin(vs), std::end(vs), comp); } template void reverseAll(Vs& vs) { std::reverse(std::begin(vs), std::end(vs)); } template V sumAll(const Vs& vs) { if constexpr (std::is_convertible::value) { return static_cast(vs); } else { V ans = 0; for (const auto& v : vs) { ans += sumAll(v); } return ans; } } template int minInd(const Vs& vs) { return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs); } template int maxInd(const Vs& vs) { return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs); } template int lbInd(const Vs& vs, const V& v) { return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs); } template int ubInd(const Vs& vs, const V& v) { return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs); } template bool contains(const Vs& vs, const V& v) { const int li = lbInd(vs, v); return (li < std::size(vs) and vs[li] == v); } template void plusAll(Vs& vs, const V& v) { for (auto& v_ : vs) { v_ += v; } } template Vec genVec(int n, F gen) { Vec ans; std::generate_n(std::back_insert_iterator(ans), n, gen); return ans; } template Vec iotaVec(int n, T offset = 0) { Vec 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 ceillog(const u64 v) { return v ? log2p1(v - 1) : 0; } constexpr u64 ceil2(const u64 v) { const int l = ceillog(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 struct Fix : F { Fix(F&& f) : F{std::forward(f)} {} template auto operator()(Args&&... args) const { return F::operator()(*this, std::forward(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; } i64 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); i64 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(i64 end) { return irange(0, end, 1); } irange per(i64 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; } static constexpr T max() { return LIMMAX; } 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; } static constexpr T max() { return LIMMAX; } 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 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 T val(T min, T max) { return std::uniform_int_distribution(min, max)(m_rng); } template Pair pair(T min, T max) { return std::minmax({val(min, max), val(min, max)}); } template Vec vec(int n, T min, T max) { return genVec(n, [&]() { return val(min, max); }); } template Vec> vvec(int n, int m, T min, T max) { return genVec>(n, [&]() { return vec(m, min, max); }); } private: Rng m_rng; }; RNG rng; RNG rng64; RNG rng_xo; RNG rng_xo64; template 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 m_used; Arr m_keys; Arr m_vals; }; template constexpr Pair extgcd(const T a, const T b) // [x,y] -> ax+by=gcd(a,b) { static_assert(std::is_signed::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 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 class modint { template static U modRef() { static u32 s_mod = 0; return s_mod; } template static U rootRef() { static u32 s_root = 0; return s_root; } template static U max2pRef() { static u32 s_max2p = 0; return s_max2p; } public: static constexpr bool isDynamic() { return (mod_ == 0); } template static constexpr std::enable_if_t mod() { return mod_; } template static std::enable_if_t mod() { return modRef(); } template static constexpr std::enable_if_t root() { return root_; } template static std::enable_if_t root() { return rootRef(); } template static constexpr std::enable_if_t max2p() { return max2p_; } template static std::enable_if_t max2p() { return max2pRef(); } template static void setMod(std::enable_if_t m) { modRef() = m; } template static void setRoot(std::enable_if_t r) { rootRef() = r; } template static void setMax2p(std::enable_if_t 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 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 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 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 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 using modint_dynamic = modint<0, 0, id>; template class modint64 { template static U modRef() { static u64 s_mod = 0; return s_mod; } template static U rootRef() { static u64 s_root = 0; return s_root; } template static U max2pRef() { static u64 s_max2p = 0; return s_max2p; } public: static constexpr bool isDynamic() { return (mod_ == 0); } template static constexpr std::enable_if_t mod() { return mod_; } template static std::enable_if_t mod() { return modRef(); } template static constexpr std::enable_if_t root() { return root_; } template static std::enable_if_t root() { return rootRef(); } template static constexpr std::enable_if_t max2p() { return max2p_; } template static std::enable_if_t max2p() { return max2pRef(); } template static void setMod(std::enable_if_t m) { modRef() = m; } template static void setRoot(std::enable_if_t r) { rootRef() = r; } template static void setMax2p(std::enable_if_t 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 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 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 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 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 using modint64_dynamic = modint64<0, 0, id>; template bool millerRabin(u64 n, const Vec& 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(n, {2, 7, 61}); } else { mint64::setMod(n); return millerRabin(n, {2, 325, 9375, 28178, 450775, 9780504}); } } template 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(0, n - 2) + 2; c = rng64.val(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 primeFactors(u64 n) { using mint = modint_dynamic<287687412>; using mint64 = modint64_dynamic<4832432>; Map 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(x); } else { mint64::setMod(x); p = pollardRho(x); } if (p == x) { ans[p]++; return; } dfs(p), dfs(x / p); })(n); return ans; } Vec divisors(const u64 n) { const auto fs = primeFactors(n); Vec 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 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 (auto _temp_name_0 [[maybe_unused]] : rep(e)) { 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 (auto _temp_name_1 [[maybe_unused]] : rep(Q - 1)) { pEraser = pEraser.pow(p); } const mint ipEraser = pEraser.inv(); IntDict 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 : rep(Q)) { 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 (auto _temp_name_2 [[maybe_unused]] : rep(l - e)) { pEraser2 = pEraser2.pow(p); } X *= pEraser2, Error *= pEraser2.pow(pe); } A = X; } return A; } class Printer { public: Printer(Ostream& os = std::cout) : m_os{os} { m_os << std::fixed << std::setprecision(15); } template int operator()(const Args&... args) { dump(args...); return 0; } template int ln(const Args&... args) { dump(args...), m_os << '\n'; return 0; } template int el(const Args&... args) { dump(args...), m_os << std::endl; return 0; } private: template void dump(const T& v) { m_os << v; } template void dump(const Vec& vs) { for (const int i : rep(vs.size())) { m_os << (i ? " " : ""), dump(vs[i]); } } template void dump(const Vec>& vss) { for (const int i : rep(vss.size())) { m_os << (i ? "\n" : ""), dump(vss[i]); } } template int dump(const T& v, const Ts&... args) { dump(v), m_os << ' ', dump(args...); return 0; } Ostream& m_os; }; Printer out; class Scanner { public: Scanner(Istream& is = std::cin) : m_is{is} { m_is.tie(nullptr)->sync_with_stdio(false); } template T val() { T v; return m_is >> v, v; } template T val(T offset) { return val() - offset; } template Vec vec(int n) { return genVec(n, [&]() { return val(); }); } template Vec vec(int n, T offset) { return genVec(n, [&]() { return val(offset); }); } template Vec> vvec(int n, int m) { return genVec>(n, [&]() { return vec(m); }); } template Vec> vvec(int n, int m, const T offset) { return genVec>(n, [&]() { return vec(m, offset); }); } template auto tup() { return Tup{val()...}; } template auto tup(const Args&... offsets) { return Tup{val(offsets)...}; } private: Istream& m_is; }; Scanner in; using mint = modint64_dynamic<0>; int main() { const int T = in.val(); for (int t : rep(T)) { const auto [P, K, Y] = in.tup(); 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; }