#include using namespace std; #ifndef CLASS_MODINT #define CLASS_MODINT #include template class modint { private: std::uint32_t n; public: modint() : n(0) {}; modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {}; static constexpr std::uint32_t get_mod() { return mod; } std::uint32_t get() const { return n; } bool operator==(const modint& m) const { return n == m.n; } bool operator!=(const modint& m) const { return n != m.n; } modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; } modint operator+(const modint& m) const { return modint(*this) += m; } modint operator-(const modint& m) const { return modint(*this) -= m; } modint operator*(const modint& m) const { return modint(*this) *= m; } modint inv() const { return (*this).pow(mod - 2); } modint pow(std::uint64_t b) const { modint ans = 1, m = modint(*this); while (b) { if (b & 1) ans *= m; m *= m; b >>= 1; } return ans; } }; #endif // CLASS_MODINT using mint = modint<998244353>; long long mygcd(long long x, long long y) { if (y == 0) { return x; } return mygcd(y, x % y); } array merge(long long X, const array& v1, const array& v2) { array res = { mint(0), mint(0) }; res[1] += v1[1] * v2[1]; res[0] += v1[0] * v2[1]; res[0] += v1[1] * v2[0]; res[0] += v1[0] * v2[0] * (X - 2); res[1] += v1[0] * v2[0] * (X - 1); return res; } mint solve(long long N, long long M, long long K) { long long cur = 1; vector seq = { 1 }; while (true) { cur = mygcd(cur * K, M); if (cur == seq.back()) { break; } seq.push_back(cur); } if (seq.size() > N) { seq.resize(N); } int V = seq.size(); seq.push_back(K); vector d(V); for (int i = 0; i < V; i++) { d[i] = seq[i + 1] / seq[i]; } vector > dp(V); dp[0] = { mint(1) }; for (int i = 1; i < V; i++) { dp[i].resize(i + 1); for (int j = 0; j < i; j++) { dp[i][j] += dp[i - 1][j] * seq[i - 1]; dp[i][j + 1] += dp[i - 1][j]; } for (int j = 0; j <= i; j++) { dp[i][j] *= (j >= 1 ? mint(d[i - 1]).pow(j - 1) : mint(1)); } } array ini = { mint(0), mint(0) }; for (int i = 0; i < V; i++) { array sub; sub[0] = dp[V - 1][i] * (i >= 1 ? mint(d[V - 1]).pow(i - 1) : mint(1)); sub[1] = dp[V - 1][i] * (i >= 1 ? mint(d[V - 1]).pow(i - 1) : mint(0)); if (i % 2 == 0) { ini[0] += sub[0]; ini[1] += sub[1]; } else { ini[0] -= sub[0]; ini[1] -= sub[1]; } } array g = { seq[V - 1], seq[V - 1] }; g[1] -= 1; array v = { mint(0), mint(1) }; long long X = M / seq[V - 1]; long long rem = N - V; while (rem >= 1) { if (rem % 2 == 1) { v = merge(X, g, v); } g = merge(X, g, g); rem /= 2; } array ans = merge(X, ini, g); return ans[1]; } int main() { long long N, M, K; cin >> N >> M >> K; mint ans = solve(N, M, K); cout << ans.get() << endl; return 0; }