#include using namespace std; #include using namespace atcoder; #define rep2(i, m, n) for (int i = (m); i < (n); ++i) #define rep(i, n) rep2(i, 0, n) #define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i) #define drep(i, n) drep2(i, n, 0) // https://opt-cp.com/fps-implementation/ template struct FormalPowerSeries : vector { using vector::vector; using vector::operator=; using F = FormalPowerSeries; F operator-() const { F res(*this); for (auto &e : res) e = -e; return res; } F &operator*=(const T &g) { for (auto &e : *this) e *= g; return *this; } F &operator/=(const T &g) { assert(g != T(0)); *this *= g.inv(); return *this; } F &operator+=(const F &g) { int n = (*this).size(), m = g.size(); (*this).resize(max(n, m)); rep(i, m) (*this)[i] += g[i]; return *this; } F &operator-=(const F &g) { int n = (*this).size(), m = g.size(); (*this).resize(max(n, m)); rep(i, m) (*this)[i] -= g[i]; return *this; } F &operator<<=(int d) { (*this).insert((*this).begin(), d, 0); return *this; } F &operator>>=(int d) { int n = (*this).size(); (*this).erase((*this).begin(), (*this).begin() + min(n, d)); return *this; } F inv(int d = -1) const { int n = (*this).size(); assert(n != 0 && (*this)[0] != 0); if (d == -1) d = n; assert(d > 0); F res{(*this)[0].inv()}; while (res.size() < d) { int m = size(res); F f(begin(*this), begin(*this) + min(n, 2*m)); F r(res); f.resize(2*m), internal::butterfly(f); r.resize(2*m), internal::butterfly(r); rep(i, 2*m) f[i] *= r[i]; internal::butterfly_inv(f); f.erase(f.begin(), f.begin() + m); f.resize(2*m), internal::butterfly(f); rep(i, 2*m) f[i] *= r[i]; internal::butterfly_inv(f); T iz = T(2*m).inv(); iz *= -iz; for (auto &e : f) e *= iz; res.insert(res.end(), f.begin(), f.begin() + m); } return {res.begin(), res.begin() + d}; } F &operator*=(const F &g) { *this = convolution(*this, g); return *this; } F &operator/=(const F &g) { int n = (*this).size(), m = g.size(); *this = convolution(*this, g.inv(max(n, m))); (*this).resize(n); return *this; } F operator*(const T &g) const { return F(*this) *= g; } F operator/(const T &g) const { return F(*this) /= g; } F operator+(const F &g) const { return F(*this) += g; } F operator-(const F &g) const { return F(*this) -= g; } F operator*(const F &g) const { return F(*this) *= g; } F operator/(const F &g) const { return F(*this) /= g; } F operator<<(const int d) const { return F(*this) <<= d; } F operator>>(const int d) const { return F(*this) >>= d; } void multiply_naive(const F &g) { int n = size(*this), m = size(g); (*this).resize(n+m-1); drep(i, n+m-1) { (*this)[i] *= g[0]; rep2(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j]; } } void divide_naive(const F &g) { assert(g[0] != T(0)); T ig0 = g[0].inv(); int n = size(*this), m = size(g); rep(i, n) { rep2(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j]; (*this)[i] *= ig0; } } void multiply(vector> g) { // sparse int n = (*this).size(); auto [d, c] = g.front(); if (d == 0) g.erase(g.begin()); else c = 0; drep(i, n) { (*this)[i] *= c; for (auto &[j, b] : g) { if (j > i) break; (*this)[i] += (*this)[i-j] * b; } } } void divide(vector> g) { // sparse, required: "g[0] == (0, c)" and "c != 0" int n = (*this).size(); auto [d, c] = g.front(); assert(d == 0 && c != T(0)); T ic = c.inv(); g.erase(g.begin()); rep(i, n) { for (auto &[j, b] : g) { if (j > i) break; (*this)[i] -= (*this)[i-j] * b; } (*this)[i] *= ic; } } void multiply(const int d, const T c) { // multiply (1 + cz^d) int n = (*this).size(); drep(i, n-d) (*this)[i+d] += (*this)[i] * c; } void divide(const int d, const T c) { // divide by (1 + cz^d) int n = (*this).size(); rep(i, n-d) (*this)[i+d] -= (*this)[i] * c; } T eval(const T &a) { T x(1), res(0); for (auto e : *this) res += e * x, x *= a; return res; } }; using mint = modint998244353; using fps = FormalPowerSeries; using sfps = vector>; int main() { int N, M; cin >> N >> M; fps P(N + 1, 0); for (int i = 1; i <= M; i++) { for (int k = 1; k * i <= N; k++) { P.at(k * i)++; } } fps Q(N + 1); for (int i = 0; i <= N; i++) { Q.at(i) = mint(M).pow(i); } fps R(N + 1); R.at(0) = 1; for (int i = 1; i <= N; i++) { R.at(i) = (M - 1) * mint(M).pow(i - 1); } fps G = Q / (fps(1, 1) + P * R); mint ans = Q.at(N) - G.at(N); cout << ans.val() << endl; }