#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; template struct Mat : array, N> { using M = Mat; void make_identity() { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = zero(); } } for (int i = 0; i < N; i++) { (*this)[i][i] = one(); } } M& operator+=(const M& rhs) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = add((*this)[i][j], rhs[i][j]); } } return *this; } M& operator*=(const M& rhs) { static M temp; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { temp[i][j] = zero(); } } for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { for (int k = 0; k < N; k++) { temp[i][k] = add(temp[i][k], mul((*this)[i][j], rhs[j][k])); } } } *this = temp; return *this; } template void inplace_pow(I k) { assert(k >= 0); static M temp; temp = *this; make_identity(); while (k) { if (k & 1) *this *= temp; k >>= 1; if (k) temp *= temp; } } friend ostream& operator<<(ostream& os, const M& A) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { os << A[i][j] << " \n"[j + 1 == N]; } } return os; } }; // mint mint add(mint x, mint y) { return x + y; } mint zero() { return mint(); } mint mul(mint x, mint y) { return x * y; } mint one() { return mint::raw(1); } using M = Mat; array solve(int n, int m, int mod, int k) { if (n == 0) return {1, 0}; int g = gcd(mod, k); if (g == 1) { M a; int x = m / mod; a[0] = {x - 1, m - 1 - (x - 1)}; a[1] = {x, m - 1 - x}; a.inplace_pow(n); return {a[0][0], a[0][1]}; } int mod2 = mod / g, k2 = k / g; auto a = solve(n - 1, m, mod2, k2); array na; int x = m / mod; na[0] = (x - 1) * a[0] + x * a[1]; na[1] = (m - 1 - (x - 1)) * a[0] + (m - 1 - x) * a[1]; return na; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, m, k; cin >> n >> m >> k; mint ans = solve(n, m, m, k)[0]; cout << ans.val() << '\n'; }