// May this submission get accepted! #pragma GCC optimize ("O3") #pragma GCC target ("tune=native") #pragma GCC target ("avx") #include // 汎用マクロ #define ALL_OF(x) (x).begin(), (x).end() #define REP(i,n) for (long long i=0, i##_len=(n); i=i##_end; i--) #define UNIQUE(v) do { sort((v).begin(), (v).end()); (v).erase(unique((v).begin(), (v).end()), (v).end()); } while (false) template bool chmax(T &a, const T &b) {if (a < b) {a = b; return true;} return false; } template bool chmin(T &a, const T &b) {if (a > b) {a = b; return true;} return false; } #define INF 0x7FFFFFFF #define LINF 0x7FFFFFFFFFFFFFFFLL #define Yes(q) ((q) ? "Yes" : "No") #define YES(q) ((q) ? "YES" : "NO") #define Possible(q) ((q) ? "Possible" : "Impossible") #define POSSIBLE(q) ((q) ? "POSSIBLE" : "IMPOSSIBLE") #define DUMP(q) cerr << "[DEBUG] " #q ": " << (q) << " at " __FILE__ ":" << __LINE__ << endl #define DUMPALL(q) do { cerr << "[DEBUG] " #q ": ["; REP(i, (q).size()) { cerr << (q)[i] << (i == i_len-1 ? "" : ", "); } cerr << "] at " __FILE__ ":" << __LINE__ << endl; } while (false) template T gcd(const T &a, const T &b) { return a < b ? gcd(b, a) : b ? gcd(b, a % b) : a; } template T lcm(const T &a, const T &b) { return a / gcd(a, b) * b; } // gcc拡張マクロ #define popcount __builtin_popcount #define popcountll __builtin_popcountll // エイリアス #define DANCE_ long #define ROBOT_ unsigned #define HUMAN_ signed #define CHOKUDAI_ const using ll = DANCE_ HUMAN_ DANCE_; using ull = DANCE_ ROBOT_ DANCE_; using cll = DANCE_ DANCE_ CHOKUDAI_; using ld = long double; using namespace std; // モジュール // 剰余演算 constexpr ll pdiv = 1000000007LL; // 10^9+7 ll powll(ll a, ll n) { if (n == 0) { return 1LL; } else if (n == 1) { return a % pdiv; } else { ll temp = powll(a, n/2); temp = temp * temp % pdiv; return n % 2 ? temp * a % pdiv : temp; } } inline ll invll(ll a) { return powll(a, pdiv-2); } vector fac_cache = {1}, invfac_cache = {1}; void make_fac_cache(ll a) { ll old_max = fac_cache.size() - 1; if (a > old_max) { fac_cache .resize(a+1); invfac_cache.resize(a+1); for (ll i = old_max + 1; i <= a; i++) { fac_cache[i] = fac_cache[i-1] * i % pdiv; } invfac_cache[a] = invll(fac_cache[a]); for (ll i = a-1; i > old_max; i--) { invfac_cache[i] = invfac_cache[i+1] * (i + 1) % pdiv; } } } inline ll facll(ll a) { make_fac_cache(a); return fac_cache[a]; } inline ll invfacll(ll a) { make_fac_cache(a); return invfac_cache[a]; } inline bool isoutll(ll n, ll r) { return n < 0 || r < 0 || n < r; } inline ll nPr(ll n, ll r) { return isoutll(n, r) ? 0 : facll(n) * invfacll(n-r) % pdiv; } inline ll nCr(ll n, ll r) { return isoutll(n, r) ? 0 : facll(n) * invfacll(n-r) % pdiv * invfacll(r) % pdiv; } inline ll nHr(ll n, ll r) { return nCr(n+r-1, r); } // 約数列挙 O(√N) template vector divisor(const T n) { if (n < 1) return vector(); vector r; for (long long i = 1; i * i <= n; i++) { if (n % i == 0) { r.push_back(i); if (i * i != n) r.push_back(n / i); } } return r; } // 素因数分解 O(√N) template vector factorize(T x) { if (x <= 1) return vector(); vector r; T x0 = x; while (x % 2 == 0) x /= 2, r.push_back(2); for (long long f = 3; f * f <= x0; f += 2) while (x % f == 0) x /= f, r.push_back(f); if (x > 1) r.push_back(x); return r; } // 処理内容 int main() { ll n, k; cin >> n >> k; ll g = gcd(n, k); if (g == 1) { cout << 0 << endl; return 0; } // O(√N * √N) = O(N) ll ans = 0; vector d = divisor(g); REP(i, d.size()) { if (d[i] == 1) continue; vector f = factorize(d[i]); sort(ALL_OF(f)); bool okay = true; REP(j, f.size()-1) if (f[j] == f[j+1]) { okay = false; break; } if (!okay) continue; if (f.size() % 2) { (ans += nCr(n / d[i], k / d[i])) %= pdiv; } else { (ans += pdiv - nCr(n / d[i], k / d[i])) %= pdiv; } } cout << ans << endl; }