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#include <cstdio> #include <cstdlib> #include <algorithm> #include <cstring> #include <cmath> #define INF 2000000000 using namespace std; typedef long long ll; ll g, l, prime[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}; ll dd[55], ans = -1; int e1[55] = {0}, e2[55] = {0}, cnt = 0; double lev, dis; ll (ll a, ll b){ return (!b) ? a : gcd(b, a % b); } ll mul(ll a, ll b, ll M){ ll res = 0; while(b){ if(b & 1ll) { res += a; if(res >= M) res -= M; } a <<= 1, b >>= 1; if(a >= M) a -= M; } return res; } ll modpow(ll a, ll b, ll M){ a %= M; ll res = 1; while(b){ if(b & 1ll) res = mul(res, a, M); a = mul(a, a, M), b >>= 1; } return res; } bool witness(ll a, ll n, ll t, ll u){ ll x = modpow(a, u, n); for(ll i = 1; i <= t; ++i){ ll xx = mul(x, x, n); if(xx == 1 && x != 1 && x != n - 1) return true; x = xx; } if(x != 1) return true; return false; } bool miller_rabin(ll n){ for(int i = 0; i < 10; ++i){ if(n == prime[i]) return true; else if(n % prime[i] == 0) return false; } ll t, u; for(t = 1; ; ++t) if((n - 1) % (1 << t) == 0) break; u = (n - 1) / (1 << t); for(int i = 0; i < 10; ++i) if(witness(rand() % (n - 1) + 1, n, t, u)) return false; return true; } ll rho(ll n, ll c){ ll x = modpow(rand(), rand(), n), y = x, d = 1; int k = 2; for(int i = 1; d == 1; ++i){ x = mul(x, x, n) + c; if(x >= n) x -= n; if(x > y) d = gcd(x - y, n); else d = gcd(y - x, n); if(i == k) y = x, k <<= 1; } return d; } ll Pollard(ll n){ ll d = n; while(d == n) d = rho(n, rand() % (n - 1) + 1); return d; } void addFac(ll &x, ll d, int *e){ int cur; for(cur = 0; cur < cnt; ++cur) if(dd[cur] == d) break; dd[cur] = d; do{ x /= d, e[cur]++; }while(x % d == 0); if(cur == cnt) cnt++; } void getFac(ll x, int *e){ if(!miller_rabin(x)){ ll d = Pollard(x); getFac(d, e), getFac(x / d, e); }else{ addFac(x, x, e); } } void dfs(int ind, ll x){ if(ind == cnt){ if(1.0 * x > lev && ans > x) ans = x; return ; } ll res = 1; for(int i = 0; i < e2[ind]; ++i) res *= dd[ind]; dfs(ind + 1, x * res); for(int i = e2[ind]; i < e1[ind]; ++i) res *= dd[ind]; dfs(ind + 1, x * res); } void init(){ srand(122144); } void solve(){ cnt = 0; memset(dd, 0, sizeof(dd)); memset(e1, 0, sizeof(e1)); memset(e2, 0, sizeof(e2)); if(g == l) cout << g << " " << l << endl; else{ getFac(l, e1); if(g != 1) getFac(g, e2); lev = sqrt(1.0 * l * g); ans = l, dfs(0, 1); cout << (l / ans) * g << " " << ans << endl; } } int main(){ while(scanf("%lld %lld", &g, &l) == 2){ init(); solve(); } return 0; }
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