#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define endl codeforces #define ALL(v) std::begin(v), std::end(v) #define ALLR(v) std::rbegin(v), std::rend(v) using ll = std::int64_t; using ull = std::uint64_t; using pii = std::pair; using tii = std::tuple; using pll = std::pair; using tll = std::tuple; using size_type = ssize_t; template using vec = std::vector; template using vvec = vec>; template const T& var_min(const T &t) { return t; } template const T& var_max(const T &t) { return t; } template const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); } template const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); } template void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); } template void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); } template struct multi_dim_array { using type = std::array::type, Head>; }; template struct multi_dim_array { using type = std::array; }; template using mdarray = typename multi_dim_array::type; template void fill_seq(T &t, F f, Args... args) { if constexpr (std::is_invocable::value) { t = f(args...); } else { for (size_type i = 0; i < t.size(); i++) fill_seq(t[i], f, args..., i); } } template vec make_v(size_type sz) { return vec(sz); } template auto make_v(size_type hs, Tail&&... ts) { auto v = std::move(make_v(std::forward(ts)...)); return vec(hs, v); } namespace init__ { struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } } init_io; } template T ceil_pow2(T bound) { T ret = 1; while (ret < bound) ret *= 2; return ret; } template T ceil_div(T a, T b) { return a / b + !!(a % b); } namespace math { template T mul_id_ele() { if constexpr (std::is_fundamental::value) { return T(1); } else { return T::mul_id_ele(); } } template T add_id_ele() { if constexpr (std::is_fundamental::value) { return T(0); } else { return T::add_id_ele(); } } template constexpr T pow(const T &n, ll k) { T ret = mul_id_ele(); T cur = n; while (k) { if (k & 1) ret *= cur; cur *= cur; k /= 2; } return ret; } template typename std::enable_if::value, T>::type gcd(T a, T b) { return b ? gcd(a % b, b) : a; } } namespace math { template struct Modint { constexpr Modint(ll x) noexcept : x((Mod + x % Mod) % Mod) { } constexpr Modint() noexcept : Modint(0) { } constexpr static Modint add_id_ele() { return Modint(0); } constexpr static Modint mul_id_ele() { return Modint(1); } constexpr ll& value() noexcept { return x; } constexpr ll value() const noexcept { return x; } constexpr Modint& operator+=(const Modint &oth) noexcept { x += oth.value(); if (Mod <= x) x -= Mod; return *this; } constexpr Modint& operator-=(const Modint &oth) noexcept { x += Mod - oth.value(); if (Mod <= x) x -= Mod; return *this; } constexpr Modint& operator*=(const Modint &oth) noexcept { x *= oth.value(); x %= Mod; return *this; } constexpr Modint& operator/=(const Modint &oth) noexcept { x *= oth.inv().value(); x %= Mod; return *this; } constexpr Modint operator+(const Modint &oth) const noexcept { return Modint(x) += oth; } constexpr Modint operator-(const Modint &oth) const noexcept { return Modint(x) -= oth; } constexpr Modint operator*(const Modint &oth) const noexcept { return Modint(x) *= oth; } constexpr Modint operator/(const Modint &oth) const noexcept { return Modint(x) /= oth; } constexpr Modint operator-() const noexcept { return Modint((x != 0) * (Mod - x)); } constexpr bool operator==(const Modint &oth) const noexcept { return value() == oth.value(); } template constexpr typename std::enable_if::value, const Modint&>::type operator=(T t) noexcept { (*this) = Modint(std::forward(t)); return *this; } constexpr Modint inv() const noexcept { return ::math::pow(*this, Mod - 2); } constexpr ll mod() const noexcept { return Mod; } private: ll x; }; template Modint inv(Modint m) { m.inv(); return m; } template std::istream& operator>>(std::istream &is, Modint &m) { ll v; is >> v; m = v; return is; } template std::ostream& operator<<(std::ostream &os, Modint m) { os << m.value(); return os; } } namespace math { template class Factorial { size_type maxv; vec factv, ifactv; public: Factorial(ssize_t maxv) : maxv(maxv), factv(maxv + 1), ifactv(maxv + 1) { factv[0] = T(1); for (ll i = 1; i <= maxv; i++) factv[i] = factv[i - 1] * i; ifactv.back() = factv.back().inv(); for (ll i = maxv - 1; 0 <= i; i--) ifactv[i] = ifactv[i + 1] * (i + 1); } T fact(size_type n) const { return factv[n]; } T ifact(size_type n) const { return ifactv[n]; } T perm(size_type n, size_type k) const { return factv[n] * ifactv[n - k]; } T comb(size_type n, size_type k) const { return perm(n, k) * ifactv[k]; } T catalan(size_type n) const { return fact[2 * n] * ifact[n + 1] * ifact[n]; } }; } constexpr ll mod = 1e9 + 7; using mint = math::Modint; math::Factorial fa(1e6 + 10); mint solve() { ll n, k, m; std::cin >> n >> k >> m; mint ans1 = 0; vec pown(n + 10); pown[0] = 1; for (ll i = 1; i < n + 10; i++) pown[i] = pown[i - 1] * n; for (ll i = 1; i <= n; i++) { if (k % i) continue; ans1 += fa.perm(n - 1, i - 1) * pown[n - i]; } if (m == 1) return ans1; mint all = pown[n]; all -= ans1; return all * mint(n - 1).inv(); } int main() { std::cout << solve() << "\n"; return 0; }