#include //////////// // ModInt // //////////// // 四則演算の最も左に存在する値がModIntでなければキャストでバグる // 例えばx = mint * 1000;やx = ModInt(1000) * mint;はいいがx = 1000 * mint;は駄目。 template class ModInt { private: int64_t integer_; public: constexpr ModInt(const int64_t initial_number = 0) : integer_(initial_number){} // 四則演算 constexpr ModInt operator+(const ModInt& operand) const { ModInt ret{this->integer_ + operand.integer_}; if (ret.integer_ >= mod_) ret.integer_ -= mod_; return ret; } constexpr ModInt operator-(const ModInt& operand) const { ModInt ret{this->integer_ - operand.integer_}; if (ret.integer_ < 0) ret.integer_ += mod_; return ret; } constexpr ModInt operator*(const ModInt& operand) const { return {this->integer_ * operand.integer_ % mod_}; } constexpr ModInt operator/(const ModInt& operand) const { return *this * (operand ^ (mod_ - 2)); } // 単項演算子 constexpr ModInt& operator++() { if (integer_ + 1 == mod_) integer_ = 0; else integer_++; return *this; } constexpr ModInt& operator--() { if (integer_ == 0) integer_ = mod_ - 1; else integer_--; return *this; } constexpr ModInt operator+() { return *this; } constexpr ModInt operator-() { if (integer_ == 0) return ModInt(0ll); else return ModInt(mod_ - integer_); } // 累乗 constexpr ModInt operator^(const int64_t operand) const { ModInt ret{1}, pow_ope{this->integer_}; for (int64_t pow{operand}; pow > 0; pow >>= 1) { if (pow & 1) ret *= pow_ope; pow_ope *= pow_ope; } return ret; } // 代入 constexpr ModInt& operator=(const ModInt& operand) { this->integer_ = operand.integer_; return *this; } constexpr ModInt& operator+=(const ModInt& operand) { *this = *this + operand; return *this; } constexpr ModInt& operator-=(const ModInt& operand) { *this = *this - operand; return *this; } constexpr ModInt& operator*=(const ModInt& operand) { *this = *this * operand; return *this; } constexpr ModInt& operator/=(const ModInt& operand) { *this = *this / operand; return *this; } // その他 constexpr operator int64_t() { return integer_; } constexpr ModInt getOne() const { return ModInt(1ll); } constexpr ModInt getZero() const { return ModInt(0ll); } }; using Mint = ModInt<>; //////////////// // 組み合わせ // /////////////// template class Combination { public: std::array, max_ + 1> inv, fact, finv; Combination() { inv[0] = inv[1] = fact[0] = fact[1] = finv[0] = finv[1] = 1; for (int num{2}; num <= max_; num++) { inv[num] = (mod_ - (int64_t)inv[mod_ % num] * (mod_ / num) % mod_) % mod_; fact[num] = num * fact[num - 1] % mod_; finv[num] = inv[num] * finv[num - 1] % mod_; } } constexpr ModInt getCombi(const int n, const int r) const { if (r < 0 || n < 0 || n - r < 0) return 0; return fact[n] * finv[r] * finv[n - r]; } constexpr ModInt getPerm(const int n, const int r) const { if (r < 0 || n < 0 || n - r < 0) return 0; return fact[n] * finv[n - r]; } }; Combination<1'000'000'007, 1'000'000> combi; int64_t calcGCD(int64_t a, int64_t b) { while (a) { b %= a; std::swap(a, b); } return b; } int main() { int64_t N, K; scanf("%lld%lld", &N, &K); std::vector table(N + 1); for (int64_t i{N}; i > 1; i--) { if (N % i > 0 || K % i > 0) continue; table[i] = combi.getCombi(N / i, K / i); for (int64_t j{2 * i}; j <= N; j += i) table[i] -= table[j]; } Mint sum; for (int i{2}; i <= N; i++) sum += table[i]; std::cout << sum << std::endl; return 0; }