//#define NDEBUG #include #include #include #include #include namespace n91 { using i8 = std::int_fast8_t; using i32 = std::int_fast32_t; using i64 = std::int_fast64_t; using u8 = std::uint_fast8_t; using u32 = std::uint_fast32_t; using u64 = std::uint_fast64_t; using isize = std::ptrdiff_t; using usize = std::size_t; constexpr usize operator"" _z(unsigned long long x) noexcept { return static_cast(x); } template class integral_iterator { public: using difference_type = T; using value_type = T; using pointer = const value_type *; using reference = value_type; using iterator_category = std::random_access_iterator_tag; private: using self_type = integral_iterator; value_type i; public: constexpr integral_iterator() noexcept : i() {} explicit constexpr integral_iterator(const value_type i) noexcept : i(i) {} constexpr self_type operator++(int) noexcept { return self_type(i++); } constexpr self_type operator--(int) noexcept { return self_type(i--); } constexpr self_type operator[](const difference_type rhs) const noexcept { return self_type(i + rhs); } constexpr self_type &operator++() noexcept { ++i; return *this; } constexpr self_type &operator--() noexcept { --i; return *this; } constexpr reference operator*() const noexcept { return i; } constexpr self_type operator+(const difference_type rhs) const noexcept { return self_type(i + rhs); } constexpr self_type operator-(const difference_type rhs) const noexcept { return self_type(i - rhs); } constexpr difference_type operator-(const self_type rhs) const noexcept { return i - rhs.i; } constexpr bool operator<(const self_type rhs) const noexcept { return i < rhs.i; } constexpr bool operator<=(const self_type rhs) const noexcept { return i <= rhs.i; } constexpr bool operator>(const self_type rhs) const noexcept { return i > rhs.i; } constexpr bool operator>=(const self_type rhs) const noexcept { return i >= rhs.i; } constexpr bool operator==(const self_type rhs) const noexcept { return i == rhs.i; } constexpr bool operator!=(const self_type rhs) const noexcept { return i != rhs.i; } constexpr self_type &operator+=(const difference_type rhs) noexcept { i += rhs; return *this; } constexpr self_type &operator-=(const difference_type rhs) noexcept { i -= rhs; return *this; } }; template constexpr integral_iterator make_int_itr(const T i) noexcept { return integral_iterator(i); } class rep { const usize f, l; public: constexpr rep(const usize f, const usize l) noexcept : f(f), l(l) {} constexpr auto begin() const noexcept { return make_int_itr(f); } constexpr auto end() const noexcept { return make_int_itr(l); } }; class revrep { const usize f, l; public: revrep(const usize f, const usize l) noexcept : f(l), l(f) {} auto begin() const noexcept { return std::make_reverse_iterator(make_int_itr(f)); } auto end() const noexcept { return std::make_reverse_iterator(make_int_itr(l)); } }; template auto md_vec(const usize n, const T &value) { return std::vector(n, value); } template auto md_vec(const usize n, Args... args) { return std::vector(n, md_vec(args...)); } template constexpr T difference(const T &a, const T &b) { return a < b ? b - a : a - b; } template T scan() { T ret; std::cin >> ret; return ret; } } // namespace n91 #include #include #include #include #include namespace n91 { template class array_matrix : public std::array, M> { public: array_matrix() { std::for_each(this->begin(), this->end(), [](auto &row) { std::fill(row.begin(), row.end(), static_cast(0)); }); } array_matrix(std::initializer_list> il) { assert(il.size() == M); auto ar_itr = this->begin(); const auto ar_end = this->end(); auto il_itr = il.begin(); while (ar_itr != ar_end) { assert(il_itr->size() == N); std::copy(il_itr->begin(), il_itr->end(), ar_itr->begin()); ++ar_itr; ++il_itr; } } array_matrix &operator*=(const array_matrix &rhs) { return *this = *this * rhs; } }; template array_matrix operator*(const array_matrix &lhs, const array_matrix &rhs) { array_matrix ret = {}; for (std::size_t i = static_cast(0); i != L; ++i) { for (std::size_t j = static_cast(0); j != M; ++j) { for (std::size_t k = static_cast(0); k != N; ++k) { ret[i][k] += lhs[i][j] * rhs[j][k]; } } } return ret; } template array_matrix matrix_identity() { array_matrix ret; for (std::size_t i = static_cast(0); i != N; ++i) { ret[i][i] = static_cast(1); } return ret; } } // namespace n91 #include namespace n91 { constexpr std::uint_fast64_t totient(std::uint_fast64_t x) noexcept { using u64 = std::uint_fast64_t; u64 ret = x; for (u64 i = static_cast(2); i * i <= x; ++i) { if (x % i == static_cast(0)) { ret -= ret / i; x /= i; while (x % i == static_cast(0)) { x /= i; } } } if (x != static_cast(1)) { ret -= ret / x; } return ret; } template (1)> class modint { using u64 = std::uint_fast64_t; static_assert(Modulus < static_cast(1) << static_cast(32), "Modulus must be less than 2**32"); u64 a; constexpr modint &negate() noexcept { if (a != static_cast(0)) { a = Modulus - a; } return *this; } public: constexpr modint(const u64 x = static_cast(0)) noexcept : a(x % Modulus) {} constexpr u64 &value() noexcept { return a; } constexpr const u64 &value() const noexcept { return a; } constexpr modint operator+() const noexcept { return modint(*this); } constexpr modint operator-() const noexcept { return modint(*this).negate(); } constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint &operator+=(const modint rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint &operator/=(modint rhs) noexcept { u64 exp = InverseExp; while (exp) { if (exp % static_cast(2) != static_cast(0)) { *this *= rhs; } rhs *= rhs; exp /= static_cast(2); } return *this; } constexpr bool operator==(const modint rhs) const noexcept { return a == rhs.a; } constexpr bool operator!=(const modint rhs) const noexcept { return a != rhs.a; } }; template class modint_constant { public: static constexpr T value = static_cast(v); using value_type = T; }; } // namespace n91 #include #include namespace n91 { template > constexpr T power(T base, U exp, const Operate &oper = Operate(), T iden = static_cast(1)) { while (exp != static_cast(0)) { if (exp % static_cast(2) != static_cast(0)) { iden = oper(iden, base); } exp /= static_cast(2); base = oper(base, base); } return iden; } } // namespace n91 #include namespace n91 { template class fact_binom { public: using value_type = T; using container_type = std::vector; using size_type = typename container_type::size_type; private: container_type factrial, inv_fact; public: fact_binom() : factrial(), inv_fact() {} explicit fact_binom(const size_type n) : factrial(n + 1), inv_fact(n + 1) { factrial[0] = static_cast(1); for (size_type i = 0; i != n; ++i) { factrial[i + 1] = static_cast(i + 1) * factrial[i]; } inv_fact[n] = static_cast(1) / factrial[n]; for (size_type i = n; i != 0; --i) { inv_fact[i - 1] = inv_fact[i] * static_cast(i); } } value_type operator()(const size_type n, const size_type r) const { return factrial[n] * inv_fact[r] * inv_fact[n - r]; } }; } // namespace n91 #include #include #include namespace n91 { void main_() { using mint = modint(1000000007)>; const usize n = scan(); const usize k = scan(); const fact_binom binom(n + 1_z); std::vector count(n + 1_z, 0_z); for (usize i = 2_z; i <= n; ++i) { if (count[i] == 0_z) { for (usize j = i; j <= n; j += i) { ++count[j]; } for (usize j = i * i; j <= n; j += i * i) { count[j] = 100_z; } } } mint ans = static_cast(0); for (usize i = 2_z; i <= n; ++i) { if (n % i != 0_z || k % i != 0_z || count[i] >= 100_z) { continue; } if (count[i] % 2_z == 1_z) { ans += binom(n / i, k / i); } else { ans -= binom(n / i, k / i); } } std::cout << ans.value() << std::endl; } } // namespace n91 int main() { n91::main_(); return 0; }