#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; namespace FastPrimeFactorization { template struct UnsafeMod { UnsafeMod() : x(0) {} UnsafeMod(word _x) : x(init(_x)) {} bool operator==(const UnsafeMod& rhs) const { return x == rhs.x; } bool operator!=(const UnsafeMod& rhs) const { return x != rhs.x; } UnsafeMod& operator+=(const UnsafeMod& rhs) { if ((x += rhs.x) >= mod) x -= mod; return *this; } UnsafeMod& operator-=(const UnsafeMod& rhs) { if (sword(x -= rhs.x) < 0) x += mod; return *this; } UnsafeMod& operator*=(const UnsafeMod& rhs) { x = reduce(dword(x) * rhs.x); return *this; } UnsafeMod operator+(const UnsafeMod& rhs) const { return UnsafeMod(*this) += rhs; } UnsafeMod operator-(const UnsafeMod& rhs) const { return UnsafeMod(*this) -= rhs; } UnsafeMod operator*(const UnsafeMod& rhs) const { return UnsafeMod(*this) *= rhs; } UnsafeMod pow(uint64_t e) const { UnsafeMod ret(1); for (UnsafeMod base = *this; e; e >>= 1, base *= base) { if (e & 1) ret *= base; } return ret; } word get() const { return reduce(x); } static constexpr int word_bits = sizeof(word) * 8; static word modulus() { return mod; } static word init(word w) { return reduce(dword(w) * r2); } static void set_mod(word m) { mod = m; inv = mul_inv(mod); r2 = -dword(mod) % mod; } static word reduce(dword x) { word y = word(x >> word_bits) - word((dword(word(x) * inv) * mod) >> word_bits); return sword(y) < 0 ? y + mod : y; } static word mul_inv(word n, int e = 6, word x = 1) { return !e ? x : mul_inv(n, e - 1, x * (2 - x * n)); } static word mod, inv, r2; word x; }; using uint128_t = __uint128_t; using Mod64 = UnsafeMod; template <> uint64_t Mod64::mod = 0; template <> uint64_t Mod64::inv = 0; template <> uint64_t Mod64::r2 = 0; using Mod32 = UnsafeMod; template <> uint32_t Mod32::mod = 0; template <> uint32_t Mod32::inv = 0; template <> uint32_t Mod32::r2 = 0; bool miller_rabin_primality_test_uint64(uint64_t n) { Mod64::set_mod(n); uint64_t d = n - 1; while (d % 2 == 0) d /= 2; Mod64 e{1}, rev{n - 1}; // http://miller-rabin.appspot.com/ < 2^64 for (uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) { if (n <= a) break; uint64_t t = d; Mod64 y = Mod64(a).pow(t); while (t != n - 1 && y != e && y != rev) { y *= y; t *= 2; } if (y != rev && t % 2 == 0) return false; } return true; } bool miller_rabin_primality_test_uint32(uint32_t n) { Mod32::set_mod(n); uint32_t d = n - 1; while (d % 2 == 0) d /= 2; Mod32 e{1}, rev{n - 1}; for (uint32_t a : {2, 7, 61}) { if (n <= a) break; uint32_t t = d; Mod32 y = Mod32(a).pow(t); while (t != n - 1 && y != e && y != rev) { y *= y; t *= 2; } if (y != rev && t % 2 == 0) return false; } return true; } bool is_prime(uint64_t n) { if (n == 2) return true; if (n == 1 || n % 2 == 0) return false; if (n < uint64_t(1) << 31) return miller_rabin_primality_test_uint32(n); return miller_rabin_primality_test_uint64(n); } uint64_t pollard_rho(uint64_t n) { if (is_prime(n)) return n; if (n % 2 == 0) return 2; Mod64::set_mod(n); uint64_t d; Mod64 one{1}; for (Mod64 c{one};; c += one) { Mod64 x{2}, y{2}; do { x = x * x + c; y = y * y + c; y = y * y + c; d = __gcd((x - y).get(), n); } while (d == 1); if (d < n) return d; } assert(0); } vector prime_factor(uint64_t n) { if (n <= 1) return {}; uint64_t p = pollard_rho(n); if (p == n) return {p}; auto l = prime_factor(p); auto r = prime_factor(n / p); copy(begin(r), end(r), back_inserter(l)); return l; } }; // namespace FastPrimeFactorization pair, vector> primes_lpf(const int n) { vector primes; primes.reserve(n / 10); vector lpf(n + 1); for (int i = 2; i <= n; i += 2) lpf[i] = 2; for (int i = 3; i <= n; i += 6) lpf[i] = 3; if (2 <= n) primes.push_back(2); if (3 <= n) primes.push_back(3); // 5 * x <= n, x <= floor(n / 5) const int n5 = n / 5; int x = 5; char add_next = 2; for (; x <= n5; x += add_next, add_next ^= 0x2 ^ 4) { int px = lpf[x]; if (px == 0) { lpf[x] = px = x; primes.push_back(x); } for (int i = 2;; ++i) { int q = primes[i]; int y = q * x; if (y > n) break; lpf[y] = q; if (q == px) break; } } for (; x <= n; x += add_next, add_next ^= 0x2 ^ 4) { if (lpf[x] == 0) { lpf[x] = x; primes.push_back(x); } } return {move(primes), move(lpf)}; } constexpr int PSIZE = 1000000; auto [primes, lpf] = primes_lpf(PSIZE); } int main() { ios::sync_with_stdio(false); cin.tie(0); ll l, r; cin >> l >> r; if (r - l <= 1000 * 45) { for (ll x = l; x <= r; x++) { auto ps = FastPrimeFactorization::prime_factor(x); sort(all(ps)); if (ps.size() == 4 && ps[0] != 2 && ps[0] == ps[1] && ps[1] != ps[2] && ps[2] != ps[3]) { cout << x << '\n'; return 0; } } cout << -1 << '\n'; return 0; } // int a = 3, b = 5; // l <= 45x <= r l = (l + 44) / 45; r = r / 45; for (ll x = max(7LL, l); x <= r; x++) { if (FastPrimeFactorization::miller_rabin_primality_test_uint64(x)) { cout << x * 45 << '\n'; return 0; } } assert(false); }