/*https://nyaannyaan.github.io/library/multiplicative-function/enamurate-multiplicative-function.hpp*/ #include using namespace std; #line 2 "multiplicative-function/enamurate-multiplicative-function.hpp" #line 2 "prime/prime-enumerate.hpp" vector prime_enumerate(int N) { vector sieve(N / 3 + 1, 1); for (int p = 5, d = 4, i = 1, sqn = sqrt(N); p <= sqn; p += d = 6 - d, i++) { if (!sieve[i]) continue; for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p, qe = sieve.size(); q < qe; q += r = s - r) sieve[q] = 0; } vector ret{2, 3}; for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++) if (sieve[i]) ret.push_back(p); while (!ret.empty() && ret.back() > N) ret.pop_back(); return ret; } #line 2 "template/template.hpp" using namespace std; #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 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template using minpq = priority_queue, greater>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P& operator+=(const P& r) { first += r.first; second += r.second; return *this; } P& operator-=(const P& r) { first -= r.first; second -= r.second; return *this; } P& operator*=(const P& r) { first *= r.first; second *= r.second; return *this; } template P& operator*=(const S& r) { first *= r, second *= r; return *this; } P operator+(const P& r) const { return P(*this) += r; } P operator-(const P& r) const { return P(*this) -= r; } P operator*(const P& r) const { return P(*this) *= r; } template P operator*(const S& r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T& t) { return t.size(); } template inline bool amin(T& x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T& x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector& v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector& v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector& v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector& v, const T& a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector& v, const T& a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T& t, const U& u) { return make_pair(t, u); } template vector mkrui(const vector& v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector& v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector& v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T& v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(T& v) { return next_permutation(begin(v), end(v)); } template vector> product(const vector& a) { vector> ret; vector v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } template T Power(T a, long long n, const T& I, const function& f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } template T Power(T a, long long n, const T& I = T{1}) { return Power(a, n, I, function{[](T&) -> void {}}); } template T Rev(const T& v) { T res = v; reverse(begin(res), end(res)); return res; } template vector Transpose(const vector& v) { using U = typename T::value_type; if (v.empty()) return {}; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template vector Rotate(const vector& v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } } // namespace Nyaan #line 58 "template/template.hpp" #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64& a) { return __builtin_popcountll(a); } inline int lsb(const u64& a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64& a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64& a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T& a, int i) { return (a >> i) & 1; } template inline void sbit(T& a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" #line 1 "template/inout.hpp" namespace Nyaan { template ostream& operator<<(ostream& os, const pair& p) { os << p.first << " " << p.second; return os; } template istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator<<(ostream& os, const vector& v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream& operator>>(istream& is, vector& v) { for (auto& x : v) is >> x; return is; } istream& operator>>(istream& is, __int128_t& x) { string S; is >> S; x = 0; int flag = 0; for (auto& c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream& operator>>(istream& is, __uint128_t& x) { string S; is >> S; x = 0; for (auto& c : S) { x *= 10; x += c - '0'; } return is; } ostream& operator<<(ostream& os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream& operator<<(ostream& os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T& t, U&... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T& t, const U&... u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" #line 1 "template/debug.hpp" namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template ::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template void dump(const T& t, enable_if_t::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair&); template void dump(const pair&); template void dump(const T& t, enable_if_t::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template void dump(const pair& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(std::forward(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" #line 5 "multiplicative-function/enamurate-multiplicative-function.hpp" template struct enamurate_multiplicative_function { enamurate_multiplicative_function(int _n) : ps(prime_enumerate(_n)), a(_n + 1, T()), n(_n), p(ps.size()) {} vector run() { a[1] = 1; dfs(-1, 1, 1); return a; } private: vector ps; vector a; int n, p; void dfs(int i, long long x, T y) { a[x] = y; if (y == T()) return; for (int j = i + 1; j < p; j++) { long long nx = x * ps[j]; long long dx = ps[j]; if (nx > n) break; for (int c = 1; nx <= n; nx *= ps[j], dx *= ps[j], ++c) { dfs(j, nx, y * f(dx, ps[j], c)); } } } }; /** * @brief 乗法的関数の列挙 */ #include using mint = atcoder::modint998244353; int N, M; const int maxn = 30'000'001; mint f(int n, int p, int e) { return mint(1 - p) / n; } mint s(int n) { return mint(long(n) * (n + 1)); } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); cin >> N >> M; if (N > M) swap(N, M); enamurate_multiplicative_function A(maxn); auto mu = A.run(); mint ans; for (int g = 1; g <= N; g++) { ans += mu[g] * g * g * s(N / g) * s(M / g); } ans *= mint::raw(2).inv().pow(2); cout << ans.val() << "\n"; }