#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1000000; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } modint comb3(modint n) { modint res = n; res *= n - (modint)1; res *= n - (modint)2; res *= (1 + mod) / 6; return res; } /*modint mem[1 << 18]; bool used[1 << 18]; modint calc(int len) { if (used[len])return mem[len]; used[len] = true; if (len == 0)return mem[len] = 0; for (int i = 1; i <= len; i++) { int d = len / i; int r = len % i; modint s = (modint)r * comb3(d + 1); s += (modint)(i - r) * comb3(d); mem[len] += s; } return mem[len]; }*/ modint mem[1 << 18]; modint calc1(int a, int b) { if (a > b)swap(a, b); modint res = (modint)2 * mem[a] + (modint)(b - a + 1) * comb3(a); //cout << "?? " < makec(int len) { vector

vp; for (int c = 1; c <= len; c++) { int d = len / c; int r = len % c; if (r > 0)vp.push_back({ d + 1,r }); vp.push_back({ d,c - r }); } sort(all(vp)); vector

res; rep(i, vp.size()) { int sum = vp[i].second; while (i + 1 < vp.size() && vp[i].first == vp[i + 1].first) { i++; sum += vp[i].second; } res.push_back({ vp[i].first,sum }); } return res; } map mp; modint calc2(int n, int m) { if (n > m)swap(n, m); if (mp.find({ n,m }) != mp.end())return mp[{n, m}]; vector

cn = makec(n); vector

cm = makec(m); modint res = 0; rep(i, cn.size())rep(j, cm.size()) { modint val = calc1(cn[i].first, cm[j].first); modint num = (modint)cn[i].second * (modint)cm[j].second; res += val * num; } return mp[{n, m}]=res; } const int mn = (1 << 18); int meb[1 << 18]; bool isp[1 << 18]; void init() { fill(isp + 2, isp + mn, true); fill(meb + 1, meb + mn, 1); for (int i = 2; i < mn; i++) { if (!isp[i])continue; meb[i] *= -1; for (int j = 2 * i; j < mn; j += i) { meb[j] *= -1; isp[j] = false; if ((j / i) % i == 0)meb[j] = 0; } } rep(i, mn - 1) { mem[i + 1] = mem[i] + comb3(i); } } void solve() { ll n, m; cin >> n >> m; modint ans = 0; for (int g = 1; g <= min(n, m); g++) { if (meb[g] == 0)continue; int d1 = n / g; int r1 = n % g; int d2 = m / g; int r2 = m % g; modint dm = (ll)r1 * r2; modint csum = 0; if (r1 > 0 && r2 > 0)csum += dm * calc2(d1 + 1, d2 + 1); dm = (ll)r1 * (g - r2); if (r1 > 0)csum += (modint)dm * calc2(d1 + 1, d2); dm = (ll)(g - r1) * r2; if (r2 > 0)csum += (modint)dm * calc2(d1, d2 + 1); dm = (ll)(g - r1) * (g - r2); csum += (modint)dm * calc2(d1, d2); ans += csum * (modint)meb[g]; //cout << g << " " << csum << " " << meb[g] << "\n"; } ans *= 2; //cout << "? " << ans << "\n"; modint al = comb3(n * m) - (modint)m * comb3(n) - (modint)n * comb3(m); //cout << al << "\n"; ans = comb3(n * m) - (modint)m * comb3(n) - (modint)n * comb3(m) - ans; cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(12); //int t; cin >> t; //rep(i, t)solve(i); init(); solve(); return 0; }