#include using namespace std; #if __has_include() #include #include using bll = boost::multiprecision::cpp_int; using bdouble = boost::multiprecision::number>; using namespace boost::multiprecision; #endif #if __has_include() #define BOOST_STACKTRACE_USE_ADDR2LINE #define BOOST_STACKTRACE_ADDR2LINE_LOCATION /usr/local/opt/binutils/bin/addr2line #define _GNU_SOURCE 1 #include #endif #ifdef LOCAL_TEST namespace std { template class dvector : public std::vector { public: dvector() : std::vector() {} explicit dvector(size_t n, const T& value = T()) : std::vector(n, value) {} dvector(const std::vector& v) : std::vector(v) {} dvector(const std::initializer_list il) : std::vector(il) {} dvector(const std::string::iterator first, const std::string::iterator last) : std::vector(first, last) {} dvector(const typename std::vector::iterator first, const typename std::vector::iterator last) : std::vector(first, last) {} dvector(const typename std::vector::reverse_iterator first, const typename std::vector::reverse_iterator last) : std::vector(first, last) {} dvector(const typename std::vector::const_iterator first, const typename std::vector::const_iterator last) : std::vector(first, last) {} dvector(const typename std::vector::const_reverse_iterator first, const typename std::vector::const_reverse_iterator last) : std::vector(first, last) {} T& operator[](size_t n) { try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); } } const T& operator[](size_t n) const { try { return this->at(n); } catch (const std::exception& e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; return this->at(n); } } }; } class dbool { private: bool boolvalue; public: dbool() : boolvalue(false) {} dbool(bool b) : boolvalue(b) {} operator bool&() { return boolvalue; } operator const bool&() const { return boolvalue; } }; #define vector dvector #define bool dbool #endif #ifdef LOCAL_DEV template std::ostream& operator<<(std::ostream& s, const std::vector& v) { for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; } template std::ostream& operator<<(std::ostream& s, const std::vector>& vv) { s << "\\\n"; for (size_t i = 0; i < vv.size(); ++i){ s << vv[i] << "\n"; } return s; } template std::ostream& operator<<(std::ostream& s, const std::deque& v) { for (size_t i = 0; i < v.size(); ++i){ s << v[i]; if (i < v.size() - 1) s << "\t"; } return s; } template std::ostream& operator<<(std::ostream& s, const std::set& se) { s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::multiset& se) { s << "{ "; for (auto itr = se.begin(); itr != se.end(); ++itr){ s << (*itr) << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::array& a) { s << "{ "; for (size_t i = 0; i < N; ++i){ s << a[i] << "\t"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::map& m) { s << "{\n"; for (auto itr = m.begin(); itr != m.end(); ++itr){ s << "\t" << (*itr).first << " : " << (*itr).second << "\n"; } s << "}"; return s; } template std::ostream& operator<<(std::ostream& s, const std::pair& p) { return s << "(" << p.first << ", " << p.second << ")"; } class SIGFPE_exception : std::exception {}; class SIGSEGV_exception : std::exception {}; void catch_SIGFPE([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGFPE_exception(); } void catch_SIGSEGV([[maybe_unused]] int e) { std::cerr << boost::stacktrace::stacktrace() << '\n'; throw SIGSEGV_exception(); } signed convertedmain(); signed main() { signal(SIGFPE, catch_SIGFPE); signal(SIGSEGV, catch_SIGSEGV); return convertedmain(); } #define main() convertedmain() void debug_impl() { std::cerr << '\n'; } template void debug_impl(Head head, Tail... tail) { std::cerr << " " << head << (sizeof...(tail) ? "," : ""); debug_impl(tail...); } #define debug(...) do { std::cerr << "(" << #__VA_ARGS__ << ") ="; debug_impl(__VA_ARGS__); } while (false) #else #define debug(...) do {} while (false) #endif //#define int long long using ll = long long; //constexpr int INF = (ll)1e9 + 7;//INT_MAX=(1<<31)-1=2147483647 constexpr ll INF = (ll)1e18;//(1LL<<63)-1=9223372036854775807 constexpr ll MOD = (ll)1e9 + 7; constexpr double EPS = 1e-9; constexpr ll dx[4] = {1, 0, -1, 0}; constexpr ll dy[4] = {0, 1, 0, -1}; constexpr ll dx8[8] = {1, 0, -1, 0, 1, 1, -1, -1}; constexpr ll dy8[8] = {0, 1, 0, -1, 1, -1, 1, -1}; #define rep(i, n) for(ll i=0, i##_length=(n); i< i##_length; ++i) #define repeq(i, n) for(ll i=1, i##_length=(n); i<=i##_length; ++i) #define rrep(i, n) for(ll i=(n)-1; i>=0; --i) #define rrepeq(i, n) for(ll i=(n) ; i>=1; --i) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() void p() { std::cout << '\n'; } template void p(Head head, Tail... tail) { std::cout << head << (sizeof...(tail) ? " " : ""); p(tail...); } template inline void pv(std::vector& v) { for(ll i=0, N=v.size(); i inline bool chmax(T& a, T b) { return a < b && (a = b, true); } template inline bool chmin(T& a, T b) { return a > b && (a = b, true); } template inline void uniq(std::vector& v) { v.erase(std::unique(v.begin(), v.end()), v.end()); } /*-----8<-----template-----8<-----*/ //ミラーラビン素数判定法とポラード・ロー法のコードは http://quiz.fuqinho.net/blog/2012/06/12/poj-2429-gcd-and-lcm-inverse/ より // return (a * b) % m ll mod_mult(ll a, ll b, ll m) { ll res = 0; ll exp = a % m; while (b) { if (b & 1) { res += exp; if (res > m) res -= m; } exp <<= 1; if (exp > m) exp -= m; b >>= 1; } return res; } // return (a ^ b) % m ll mod_exp(ll a, ll b, ll m) { ll res = 1; ll exp = a % m; while (b) { if (b & 1) res = mod_mult(res, exp, m); exp = mod_mult(exp, exp, m); b >>= 1; } return res; } // ミラー-ラビン素数判定法 bool miller_rabin(ll n, ll times) { if (n < 2) return false; if (n == 2) return true; if (!(n & 1)) return false; ll q = n - 1; int k = 0; while (q % 2 == 0) { k++; q >>= 1; } // n - 1 = 2^k * q (qは奇素数) // nが素数であれば、下記のいずれかを満たす // (i) a^q ≡ 1 (mod n) // (ii) a^q, a^2q,..., a^(k-1)q のどれかがnを法として-1 // // なので、逆に(i)(ii)いずれも満たしていない時は合成数と判定できる // for (int i = 0; i < times; i++) { ll a = rand() % (n - 1) + 1; // 1,..,n-1からランダムに値を選ぶ ll x = mod_exp(a, q, n); // (i)をチェック if (x == 1) continue; // (ii)をチェック bool found = false; for (int j = 0; j < k; j++) { if (x == n - 1) { found = true; break; } x = mod_mult(x, x, n); } if (found) continue; return false; } return true; } ll get_gcd(ll n, ll m) { if (n < m) swap(n, m); while (m) { swap(n, m); m %= n; } return n; } // ポラード・ロー素因数分解法 ll pollard_rho(ll n, int c) { ll x = 2; ll y = 2; ll d = 1; while (d == 1) { x = mod_mult(x, x, n) + c; y = mod_mult(y, y, n) + c; y = mod_mult(y, y, n) + c; d = get_gcd((x - y >= 0 ? x - y : y - x), n); } if (d == n) return pollard_rho(n, c + 1); return d; } vector primes; vector is_prime; // 小さい素数(MAX_PRIMEまで)は先に用意しとく void init_primes(ll MAX_PRIME) { is_prime.assign(MAX_PRIME + 1, true); is_prime[0] = is_prime[1] = false; for (int i = 2; i <= MAX_PRIME; i++) { if (is_prime[i]) { primes.push_back(i); for (int j = i * 2; j <= MAX_PRIME; j += i) { is_prime[j] = false; } } } } // 素数かどうか判定。大きければミラーラビンを使う bool isPrime(ll n) { if (n < (ll)is_prime.size()) return is_prime[n]; else return miller_rabin(n, 7); } // 素因数分解する。小さい数は用意した素数で試し割り、大きければポラード・ロー void factorize(ll n, map& factors) { if (isPrime(n)) { factors[n]++; } else { for (int i = 0; i < (int)primes.size(); i++) { int p = primes[i]; while (n % p == 0) { factors[p]++; n /= p; } } if (n != 1) { if (isPrime(n)) { factors[n]++; } else { ll d = pollard_rho(n, 1); factorize(d, factors); factorize(n / d, factors); } } } } /*-----8<-----library-----8<-----*/ void solve() { init_primes(100); ll A,B; cin>>A>>B; ll g=gcd(A,B); map m; factorize(g,m); for(auto&& x:m){ if((x.second+1)%2==0){ p("Even");return; } } p("Odd"); } signed main() { solve(); return 0; }