#include #pragma GCC diagnostic ignored "-Wsign-compare" #pragma GCC diagnostic ignored "-Wsign-conversion" #define NDEBUG using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; using uint = unsigned int; using usize = std::size_t; using ll = long long; using ull = unsigned long long; using ld = long double; template constexpr T popcount(const T u) { return u ? static_cast(__builtin_popcountll(static_cast(u))) : static_cast(0); } template constexpr T log2p1(const T u) { return u ? static_cast(64 - __builtin_clzll(static_cast(u))) : static_cast(0); } template constexpr T msbp1(const T u) { return log2p1(u); } template constexpr T lsbp1(const T u) { return __builtin_ffsll(u); } template constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast(u); } template constexpr bool ispow2(const T u) { return u and (static_cast(u) & static_cast(u - 1)) == 0; } template constexpr T ceil2(const T u) { return static_cast(1) << clog(u); } template constexpr T floor2(const T u) { return u == 0 ? static_cast(0) : static_cast(1) << (log2p1(u) - 1); } template constexpr bool btest(const T mask, const usize ind) { return ((static_cast(mask) >> ind) & static_cast(1)); } template constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast(0) : static_cast((static_cast(mask) << (64 - ind)) >> (64 - ind)); } template bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); } template bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); } constexpr unsigned int mod = 1000000007; template constexpr T inf_v = std::numeric_limits::max() / 4; template constexpr Real pi_v = Real{3.141592653589793238462643383279502884}; /** * http://xoshiro.di.unimi.it/xoshiro128starstar.c * http://xoshiro.di.unimi.it/xoshiro256starstar.c * http://xoshiro.di.unimi.it/splitmix64.c */ class xoshiro { public: using result_type = uint32_t; static constexpr result_type min() { return std::numeric_limits::min(); } static constexpr result_type max() { return std::numeric_limits::max(); } xoshiro() : xoshiro(std::random_device{}()) {} xoshiro(uint64_t seed) { uint64_t z = 0; for (int i = 0; i < 4; i++) { z = (seed += 0x9e3779b97f4a7c15), z = (z ^ (z >> 33)) * 0x62A9D9ED799705F5, z = (z ^ (z >> 28)) * 0xCB24D0A5C88C35B3, s[i] = static_cast(z >> 32); } } result_type operator()() { const result_type result = rotl(s[1] * 5, 7) * 9, t = s[1] << 9; return s[2] ^= s[0], s[3] ^= s[1], s[1] ^= s[2], s[0] ^= s[3], s[2] ^= t, s[3] = rotl(s[3], 11), result; } void discard(const usize rep) { for (usize i = 0; i < rep; i++) { (*this)(); } } private: result_type s[4]; static result_type rotl(const result_type x, const int k) { return (x << k) | (x >> (32 - k)); } }; class xoshiro_64 { public: using result_type = uint64_t; static constexpr result_type min() { return std::numeric_limits::min(); } static constexpr result_type max() { return std::numeric_limits::max(); } xoshiro_64() : xoshiro_64(std::random_device{}()) {} xoshiro_64(uint64_t seed) { uint64_t z = 0; for (int i = 0; i < 4; i++) { z = (seed += 0x9e3779b97f4a7c15), z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9, z = (z ^ (z >> 27)) * 0x94d049bb133111eb, s[i] = static_cast(z ^ (z >> 31)); } } result_type operator()() { const result_type result = rotl(s[1] * 5, 7) * 9, t = s[1] << 17; return s[2] ^= s[0], s[3] ^= s[1], s[1] ^= s[2], s[0] ^= s[3], s[2] ^= t, s[3] = rotl(s[3], 45), result; } void discard(const usize rep) { for (usize i = 0; i < rep; i++) { (*this)(); } } private: result_type s[4]; static result_type rotl(const result_type x, const int k) { return (x << k) | (x >> (64 - k)); } }; template class rng_base { public: using rng_type = Rng; using result_type = typename rng_type::result_type; static constexpr result_type min() { return rng_type::min(); } static constexpr result_type max() { return rng_type::max(); } rng_base() : rng_base(std::random_device{}()) {} rng_base(const u64 seed) : rng(seed) {} ~rng_base() = default; result_type operator()() { return rng(); } template Int uniform_int(const Int max) { static_assert(std::is_integral::value, "Integer type is needed."); if (ispow2(max + 1)) { return static_cast(rng() & max); } const result_type mask = static_cast(ceil2(static_cast(max + 1))) - 1; while (true) { const Int ans = static_cast(rng() & mask); if (ans <= max) { return ans; } } } template Int uniform_int(const Int min, const Int max) { return min + uniform_int(static_cast(max - min)); } bool uniform_bool() { return uniform_int(0, 1); } template Real uniform_real() { static_assert(std::is_floating_point::value, "FloatingPoint type is needed."); return static_cast(uniformInt(~static_cast(0)) / static_cast(~static_cast(0))); } template Real uniform_real(const Real min, const Real max) { return assert(min <= max), uniform_real() * (max - min) + min; } template std::pair uniform_int_pair(const Int min, const Int max) { return std::minmax(uniform_int(min, max), uniform_int(min, max)); } template std::vector uniform_int_vec(const std::size_t size, const Int min, const Int max) { std::vector v(size); for (std::size_t i = 0; i < size; i++) { v[i] = uniformInt(min, max); } return v; } template std::vector uniform_real_vec(const std::size_t size, const Real min, const Real max) { std::vector v(size); for (std::size_t i = 0; i < size; i++) { v[i] = uniformReal(min, max); } return v; } void discard(const usize rep) { rng.discard(rep); } private: Rng rng; }; using rng_mt = rng_base; using rng_mt64 = rng_base; using rng_xoshiro = rng_base; using rng_xoshiro64 = rng_base; rng_mt g_rng_mt; rng_mt64 g_rng_mt64; rng_xoshiro g_rng_xo; rng_xoshiro64 g_rng_xo64; template T read() { T v; return std::cin >> v, v; } template std::vector read_vec(const std::size_t size) { std::vector v(size); for (auto& e : v) { std::cin >> e; } return v; } #define SHOW(...) static_cast(0) template std::vector make_v(const std::size_t size, T v) { return std::vector(size, v); } template auto make_v(const std::size_t size, Args... args) { return std::vector(size, make_v(args...)); } template T gcd(const T& a, const T& b) { return (a > b ? gcd(b, a) : a == 0 ? b : gcd(b % a, a)); } template T lcm(const T& a, const T& b) { return a / gcd(a, b) * b; } template constexpr std::pair extgcd(const T a, const T b) { if (b == 0) { return std::pair{1, 0}; } const auto g = gcd(a, b), da = std::abs(b) / g; const auto p = extgcd(b, a % b); const auto x = (da + p.second % da) % da, y = (g - a * x) / b; return {x, y}; } template constexpr T inverse(const T a, const T mod) { return extgcd(a, mod).first; } template class modint_base { public: template static std::enable_if_t mod() { return mod_ref(); } template static constexpr std::enable_if_t mod() { return mod_value; } template static void set_mod(const std::enable_if_t mod) { mod_ref() = mod; } modint_base() : v{0} {} modint_base(const ll val) : v{norm(static_cast(val % static_cast(mod()) + static_cast(mod())))} {} modint_base(const modint_base& n) : v{n()} {} explicit operator bool() const { return v != 0; } bool operator!() const { return not static_cast(*this); } modint_base& operator=(const modint_base& m) { return v = m(), (*this); } modint_base& operator=(const ll val) { return v = norm(uint(val % static_cast(mod()) + static_cast(mod()))), (*this); } friend modint_base operator+(const modint_base& m) { return m; } friend modint_base operator-(const modint_base& m) { return make(norm(mod() - m.v)); } friend modint_base operator+(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + m2.v)); } friend modint_base operator-(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + mod() - m2.v)); } friend modint_base operator*(const modint_base& m1, const modint_base& m2) { return make(static_cast(static_cast(m1.v) * static_cast(m2.v) % static_cast(mod()))); } friend modint_base operator/(const modint_base& m1, const modint_base& m2) { return m1 * inv(m2.v); } friend modint_base operator+(const modint_base& m, const ll val) { return modint_base{static_cast(m.v) + val}; } friend modint_base operator-(const modint_base& m, const ll val) { return modint_base{static_cast(m.v) - val}; } friend modint_base operator*(const modint_base& m, const ll val) { return modint_base{static_cast(m.v) * (val % static_cast(mod()))}; } friend modint_base operator/(const modint_base& m, const ll val) { return modint_base{static_cast(m.v) * inv(val)}; } friend modint_base operator+(const ll val, const modint_base& m) { return modint_base{static_cast(m.v) + val}; } friend modint_base operator-(const ll val, const modint_base& m) { return modint_base{-static_cast(m.v) + val}; } friend modint_base operator*(const ll val, const modint_base& m) { return modint_base{static_cast(m.v) * (val % static_cast(mod()))}; } friend modint_base operator/(const ll val, const modint_base& m) { return modint_base{val * inv(static_cast(m.v))}; } friend modint_base& operator+=(modint_base& m1, const modint_base& m2) { return m1 = m1 + m2; } friend modint_base& operator-=(modint_base& m1, const modint_base& m2) { return m1 = m1 - m2; } friend modint_base& operator*=(modint_base& m1, const modint_base& m2) { return m1 = m1 * m2; } friend modint_base& operator/=(modint_base& m1, const modint_base& m2) { return m1 = m1 / m2; } friend modint_base& operator+=(modint_base& m, const ll val) { return m = m + val; } friend modint_base& operator-=(modint_base& m, const ll val) { return m = m - val; } friend modint_base& operator*=(modint_base& m, const ll val) { return m = m * val; } friend modint_base& operator/=(modint_base& m, const ll val) { return m = m / val; } friend modint_base operator^(const modint_base& m, const ll n) { return power(m.v, n); } friend modint_base& operator^=(modint_base& m, const ll n) { return m = m ^ n; } friend bool operator==(const modint_base& m1, const modint_base& m2) { return m1.v == m2.v; } friend bool operator!=(const modint_base& m1, const modint_base& m2) { return not(m1 == m2); } friend bool operator==(const modint_base& m, const ll val) { return m.v == norm(static_cast(static_cast(mod()) + val % static_cast(mod()))); } friend bool operator!=(const modint_base& m, const ll val) { return not(m == val); } friend bool operator==(const ll val, const modint_base& m) { return m.v == norm(static_cast(static_cast(mod()) + val % static_cast(mod()))); } friend bool operator!=(const ll val, const modint_base& m) { return not(m == val); } friend std::istream& operator>>(std::istream& is, modint_base& m) { ll v; return is >> v, m = v, is; } friend std::ostream& operator<<(std::ostream& os, const modint_base& m) { return os << m(); } uint operator()() const { return v; } private: template static std::enable_if_t mod_ref() { static UInt mod = 0; return mod; } static uint norm(const uint x) { return x < mod() ? x : x - mod(); } static modint_base make(const uint x) { modint_base m; return m.v = x, m; } static modint_base power(modint_base x, ull n) { modint_base ans = 1; for (; n; n >>= 1, x *= x) { if (n & 1) { ans *= x; } } return ans; } static modint_base inv(const modint_base& x) { return modint_base{inverse(static_cast(x.v), static_cast(mod()))}; } uint v; }; template using modint = modint_base; template using dynamic_modint = modint_base; /** * @brief エラストテレスの篩 * @return std::vector ans[n]:nを割り切る最大のn未満の約数(素数ならn) * @param[in] max 篩の大きさ * @details 時間計算量:O(NloglogN) */ std::vector factor_table(const usize max) { std::vector fact(max + 1); std::iota(fact.begin(), fact.end(), 0); for (usize i = 2; i <= max; i++) { if (fact[i] != i) { continue; } for (usize j = 2; i * j <= max; j++) { fact[i * j] = i; } } return fact; } std::vector moebius_table(const usize max) { const auto f_table = factor_table(max); std::vector ans(max + 1, 0); ans[1] = 1; for (usize i = 2; i <= max; i++) { usize num = 0; for (usize n = i, prev = 1; n > 1; prev = f_table[n], n /= f_table[n]) { if (prev == f_table[n]) { num = 0; break; } else { num++; } } ans[i] = num == 0 ? 0 : num % 2 == 0 ? 1 : -1; } return ans; } int main() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false); using mint = modint; const auto H = read(), W = read(); std::vector y(H, 0); for (usize g = 1; g < H; g++) { for (usize j = g; j < H; j += g) { y[g] += H - j; } } std::vector x(W, 0); for (usize g = 1; g < W; g++) { for (usize j = g; j < W; j += g) { x[g] += W - j; } } mint ans = H * (W - 1) + W * (H - 1); std::vector dp(std::min(H, W), 0); for (usize i = 1; i < std::min(H, W); i++) { dp[i] = x[i] * y[i] * 2; } const auto moebius = moebius_table(std::min(H, W)); SHOW(dp, moebius); for (usize i = 1; i < dp.size(); i++) { ans += moebius[i] * dp[i]; } std::cout << ans << std::endl; SHOW(ans); return 0; }