#include using namespace std; using lint = long long int; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define SZ(x) ((lint)(x).size()) #define POW2(n) (1LL << (n)) #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector &vec, int len) { vec.resize(len); } template void ndarray(vector &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); } template bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template istream &operator>>(istream &is, vector &vec){ for (auto &v : vec) is >> v; return is; } ///// This part below is only for debug, not used ///// template ostream &operator<<(ostream &os, const vector &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; } template ostream &operator<<(ostream &os, const deque &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; } template ostream &operator<<(ostream &os, const set &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const multiset &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const pair &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; } template ostream &operator<<(ostream &os, const map &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; } #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl; ///// END ///// /* #include #include #include using namespace __gnu_pbds; // find_by_order(), order_of_key() template using pbds_set = tree, rb_tree_tag, tree_order_statistics_node_update>; template using pbds_map = tree, rb_tree_tag, tree_order_statistics_node_update>; */ // エラトステネスの篩で(int)N以下の素数格納vector作成 vector makePrimeLst(int N) { vector ans; vector alive(N+1, 1); lint now = 2; for (; now * now <= N; now++) { if (alive[now]) ans.push_back(now); for (int t = now; t <= N; t += now) alive[t] = 0; } for (; now <= N; now++) if (alive[now]) ans.push_back(now); return ans; } // 素因数分解 map primeFactorize(lint N, const vector &primeLst) { map ans; for (auto v : primeLst) { while (!(N % v)) { N /= v; ans[v]++; } if (N == 1) return ans; } ans[N]++; return ans; // exit(1); } vector divisor(lint n, const vector &primeLst) { map factor = primeFactorize(n, primeLst); vector now{1}, nxt; for (auto pa : factor) { nxt.clear(); for (auto v : now) { REP(i, pa.second + 1) { nxt.push_back(v); v *= pa.first; } } swap(now, nxt); } return now; } int moebius(int NperD, vector& primes) { map m = primeFactorize(NperD, primes); int Max = 1; for (auto v : m) Max = max(Max, v.second); if (Max > 1) return 0; else return ((int)(m.size()) & 1) ? -1 : 1; } constexpr lint MOD = 1000000007; vector fac, facInv, inv; void facInit(int nmax) { fac = facInv = inv = vector(nmax + 1, 1); for (int i = 2; i <= nmax; i++) { fac[i] = fac[i-1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD; facInv[i] = facInv[i-1] * inv[i] % MOD; } } lint nCr(lint n, lint r) { if (n= (int)fac.size()) facInit(n); return (fac[n] * facInv[r] % MOD) * facInv[n-r] % MOD; } lint nPr(lint n, lint r) { if (n= (int)fac.size()) facInit(n); return fac[n] * facInv[n-r] % MOD; } lint power(lint x, lint n, lint mod=MOD) { lint ans = 1; while (n>0) { if (n & 1) (ans *= x) %= mod; (x *= x) %= mod; n >>= 1; } return ans; } lint doublefac(lint n) { if (n < 0) return 0; lint k = (n + 1) / 2; if (n & 1) return fac[k * 2] * power(facInv[2], k) % MOD * power(fac[k], MOD - 2) % MOD; else return fac[k] * power(facInv[2], k) % MOD; } int main() { lint N, K; cin >> N >> K; facInit(N * 2); vector primes = makePrimeLst(1000000); vector v(N + 1); FOR(c, 1, N + 1) { if (N % c or K % (N / c)) continue; int t = N / c; int u = K / t; v[c] = nCr(c, u); } vector ret(N + 1); FOR(c, 1, N + 1) if (N % c == 0) { vector divs = divisor(c, primes); for (auto d : divs) { (ret[c] += (moebius(c / d, primes) * v[d] + MOD)) %= MOD; } } cout << accumulate(ret.begin(), ret.begin() + N, 0LL) % MOD << endl; }