#include #define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i)) #define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i)) #define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i)) #define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i)) #define ALL(x) std::begin(x), std::end(x) #define dump(x) cerr << #x " = " << x << endl using namespace std; template using reversed_priority_queue = priority_queue, greater >; template inline void chmax(T & a, U const & b) { a = max(a, b); } template inline void chmin(T & a, U const & b) { a = min(a, b); } template auto make_table(X x, T a) { return vector(x, a); } template auto make_table(X x, Y y, Z z, Zs... zs) { auto cont = make_table(y, z, zs...); return vector(x, cont); } template ostream & operator << (ostream & out, vector const & xs) { REP (i, (int)xs.size() - 1) out << xs[i] << ' '; if (not xs.empty()) out << xs.back(); return out; } template struct mint { int32_t value; mint() : value() {} mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {} inline mint operator + (mint other) const { int32_t c = this->value + other.value; return mint(c >= MOD ? c - MOD : c); } inline mint operator - (mint other) const { int32_t c = this->value - other.value; return mint(c < 0 ? c + MOD : c); } inline mint operator * (mint other) const { int32_t c = (int64_t)this->value * other.value % MOD; return mint(c < 0 ? c + MOD : c); } inline mint & operator += (mint other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; } inline mint & operator -= (mint other) { this->value -= other.value; if (this->value < 0) this->value += MOD; return *this; } inline mint & operator *= (mint other) { this->value = (int64_t)this->value * other.value % MOD; if (this->value < 0) this->value += MOD; return *this; } inline mint operator - () const { return mint(this->value ? MOD - this->value : 0); } mint pow(uint64_t k) const { mint x = *this, y = 1; for (; k; k >>= 1) { if (k & 1) y *= x; x *= x; } return y; } mint inv() const { assert (value != 0); int64_t a = value, b = MOD; int64_t x = 0, y = 1; for (int64_t u = 1, v = 0; a; ) { int64_t q = b / a; x -= q * u; std::swap(x, u); y -= q * v; std::swap(y, v); b -= q * a; std::swap(b, a); } assert (value * x + MOD * y == b); assert (b == 1); return x; } inline mint operator / (mint other) const { return *this * other.inv(); } inline mint operator /= (mint other) { return *this *= other.inv(); } inline bool operator == (mint other) const { return value == other.value; } inline bool operator != (mint other) const { return value != other.value; } }; template mint operator * (int64_t value, mint n) { return mint(value) * n; } template std::ostream & operator << (std::ostream & out, mint n) { return out << n.value; } template mint fact(int n) { static std::vector > memo(1, 1); while (n >= memo.size()) { memo.push_back(memo.back() * mint(memo.size())); } return memo[n]; } template mint inv_fact(int n) { static std::vector > memo; if (memo.size() <= n) { int l = memo.size(); int r = n * 1.3 + 100; memo.resize(r); memo[r - 1] = fact(r - 1).inv(); for (int i = r - 2; i >= l; -- i) { memo[i] = memo[i + 1] * (i + 1); } } return memo[n]; } /** * @tparam MOD must be a prime * @note O(n log n) at first time, otherwise O(1) */ template mint choose(int n, int r) { assert (0 <= r and r <= n); return fact(n) * inv_fact(n - r) * inv_fact(r); } constexpr int MOD = 1e9 + 7; mint solve(int n, int k) { dump(n); dump(k); vector > f(n); REP3 (i, 1, n) { if (i != gcd(n, i)) continue; int j = n / gcd(n, i); if (k % j == 0) { f[i] = choose(i, k / j); } } REP3 (i, 1, n) { for (int j = 2 * i; j < n; j += i) { if (f[j] != 0) { f[j] -= f[i]; } } } return accumulate(ALL(f), mint(0)); } int main() { int n, k; cin >> n >> k; cout << solve(n, k) << endl; return 0; }