#line 1 "c.cpp" #include #include #define rep(i,n) for (int i = 0; i < int(n); ++i) #define repp(i,n,m) for (int i = m; i < int(n); ++i) #define reb(i,n) for (int i = int(n)-1; i >= 0; --i) #define all(v) v.begin(),v.end() using namespace std; using namespace atcoder; using ll = long long; using ull = unsigned long long; using ld = long double; using P = pair; using PL = pair; using pdd = pair; using pil = pair; using pli = pair; templateistream &operator>>(istream &is,vector &v){for(auto &e:v)is>>e;return is;} templatebool range(T a,T b,T x){return (a<=x&&xbool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));} template T rev(const T& str_or_vec){T res = str_or_vec; reverse(res.begin(),res.end()); return res; } templatebool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;} templatebool chmax(T &a,const T &b){if(avoid uniq(vector &v){sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());} templatevoid print(pair a); templatevoid print(vector v); templatevoid print(vector> v); void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } void print(unsigned int a){ printf("%u", a); } void print(unsigned long long a) { printf("%llu", a); } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } templatevoid print(pair a){print(a.first);print(),print(a.second);} templatevoid print(vector v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}} templatevoid print(vector> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())out();}} void yes(){out("Yes");} void no (){out("No");} void yn (bool t){if(t)yes();else no();} void fast_io(){cin.tie(0); ios::sync_with_stdio(0); cout< dx = {0,1,0,-1,1,1,-1,-1}; const vector dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; } // namespace noya2 using namespace noya2; using mint = modint998244353; //using mint = modint1000000007; //using mint = modint; void out(mint a){out(a.val());} void out(vector a){vector b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);} void out(vector> a){for (auto v : a) out(v);} istream &operator>>(istream &is,vector &v){for(auto &e:v){ll _x;is>>_x;e=_x;}return is;} #line 2 "math.hpp" #line 6 "math.hpp" namespace noya2{ using namespace std; using ll = long long; template T sqrt_safe(T x){ // floor(sqrt(x)) assert(x >= T(0)); if (x <= T(1)) return x; T tmp = (T)(sqrtl((long double)(x))) + T(2); while (tmp--){ if (tmp * tmp <= x) break; } return tmp; } ll mod_safe(ll a, ll m){ // m >= 1, 0 <= mod_safe(a,m) < m, mod_safe(a,m) = a (mod m) ll res = a % m; if (res < 0) res += m; return res; } ll modpow(ll x, ll n, ll mod){ x = mod_safe(x,mod); if (n == 0) return 1; ll res = modpow(x,n/2,mod); res = (res * res) % mod; if (n % 2 == 1) res = (res * x) % mod; return res; } ll naive_gcd(ll a, ll b){ return b ? naive_gcd(b, a % b) : a; } // gcd(N >= 0, 0) = N, especialy gcd(0, 0) = 0 ll gcd_safe(ll a, ll b){ return naive_gcd(abs(a),abs(b)); } ll lcm_safe(ll a, ll b){ return a / gcd_safe(a,b) * b; } void ext_gcd1_plus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax + by = 1 if (b == 0){ // a = 1 x = 1, y = 0; return ; } ext_gcd1_plus(b, a%b, y, x); x = mod_safe(x,b); y = (1 - a * x) / b; } void ext_gcd1_minus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax - by = 1 if (b == 0){ // a = 1 x = 1, y = 0; return ; } ext_gcd1_plus(b, a%b, y, x); x = mod_safe(x,b); y = (a * x - 1) / b; } pair ext_gcd(ll a, ll b, ll c){ // ax + by = c, |a|,|b|,|c| < 1e9, x <= max(|B|,|C|), y <= max(|A|,|C|) if (a < 0) return ext_gcd(-a,-b,-c); if (c < 0){ pair res = ext_gcd(a,b,-c); res.first = -res.first, res.second = -res.second; return res; } if (c == 0) return pair(0,0); if (a == 0 && b == 0) return pair(0,0); // answer not exist ll g = gcd_safe(a,b); if (c % g != 0) return pair(0,0); // answer not exist a /= g, b /= g, c /= g; ll x, y; if (b == 0) return pair(c,0); if (b > 0) ext_gcd1_plus(a,b,x,y); else ext_gcd1_minus(a,-b,x,y); x = mod_safe(x*c,abs(b)); y = (c - a * x) / b; return pair(x,y); } template T ceil_safe(T p, T q); template T floor_safe(T p, T q){ if (q < T(0)) return floor_safe(-p,-q); if (p >= T(0)) return p / q; return -ceil_safe(-p,q); } template T ceil_safe(T p, T q){ if (q < T(0)) return ceil_safe(-p,-q); if (p >= T(0)) return (p + q - 1) / q; return -floor_safe(-p,q); } struct Eratosthenes{ static vector table; Eratosthenes (int Nmax = -1) {init(Nmax);} static void init(int Nmax){ if (!table.empty()) return ; table.resize(Nmax+1,0); table[0] = 1, table[1] = 1; for (int p = 2; p <= Nmax; p++){ if (table[p] != 0) continue; for (int j = p; j <= Nmax; j += p){ table[j] = p; } } } }; vectorEratosthenes::table = vector(0); void build_eratosthenes(const int Nmax){Eratosthenes::init(Nmax);} vector> fast_prime_factorization(int N){ int pre = -1, cnt = 0; vector> res; while(true) { if (N == 1){ if (cnt > 0) res.emplace_back(pre,cnt); break; } int div = Eratosthenes::table[N]; if (pre != div){ if (cnt > 0) res.emplace_back(pre,cnt); pre = div, cnt = 1; } else cnt++; N /= div; } return res; } vector fast_divisor_enumeration(int N){ auto pes = fast_prime_factorization(N); vector res = {1}; for (auto pe : pes){ vector nres; for (auto x : res){ for (int _t = 0; _t <= pe.second; _t++){ nres.emplace_back(x); x *= pe.first; } } swap(res,nres); } return res; } bool fast_is_prime(int N){ if (N <= 1) return false; return Eratosthenes::table[N] == N; } vector mobius(int N){ vector res(N+1,0); res[1] = 1; for (int p = 2; p <= N; p++){ if (fast_is_prime(p)){ for (int i = N/p; i > 0; i--){ res[i*p] = -res[i]; } } } return res; }; vector> prime_factorization(ll N){ vector> res; ll iN = N; for (ll d = 2; d * d <= N; d++){ if (iN % d != 0) continue; if (iN == 1) break; int ie = 0; while (iN % d == 0) iN /= d, ie++; res.emplace_back(d,ie); } if (iN != 1) res.emplace_back(iN,1); return res; } vector divisor_enumeration(ll N){ vector res; for (ll d = 1; d * d <= N; d++){ if (N % d != 0) continue; res.emplace_back(d); if (d * d != N) res.emplace_back(N/d); } return res; } bool is_prime(ll N){ if (N <= 1) return false; if (N <= 3) return true; if (N % 2 == 0) return false; for (ll d = 3; d * d <= N; d += 2){ if (N % d == 0) return false; } return true; } }// namespace noya2 #line 2 "dirichlet.hpp" /* https://maspypy.com/dirichlet-積と、数論関数の累積和 */ #line 11 "dirichlet.hpp" namespace noya2{ using namespace std; using ll = long long; using ld = long double; struct Dirichlet { int N; vector primes, factor, mu; Dirichlet (int Nmax = 1'000'000) : N(Nmax), factor(Nmax+1,0), mu(Nmax+1,1) { for(int n = 2; n <= N; n++) { if(factor[n] == 0) { primes.push_back(n); factor[n] = n; mu[n] = -1; } for(int p : primes) { if(n * p > N || p > factor[n]) break; factor[n * p] = p; mu[n * p] = p == factor[n] ? 0 : -mu[n]; } } } }; template T floor_sqrt(T x){ // floor(sqrt(x)) if (x <= T(1)) return x; T tmp = (T)(sqrtl((long double)(x))) + T(2); while (tmp--){ if (tmp * tmp <= x) break; } return tmp; } // proposition 4 template pair,vector> multiply_sparce(ll N, vector &a, vector &b, vector &A, vector &B){ ll K = a.size()-1, L = A.size()-1; // N <= K * L , K >= floor_sqrt(N) vector c(K+1,0); for (int i = 1; i <= K; i++){ for (int j = 1; i * j <= K; j++){ c[i*j] += a[i] * b[j]; } } vector arui(K+1,0), brui(K+1,0); for (int i = 1; i <= K; i++){ arui[i] = arui[i-1] + a[i]; brui[i] = brui[i-1] + b[i]; } ld Nd = N; vector C(L+1,0); for (ll l = 1; l <= L; l++){ ll n = Nd / ld(l); ll m = floor_sqrt(n); for (ll i = 1; i <= m; i++){ ll il = i*l; if (il <= L){ C[l] += a[i] * B[il]; // B[i] = B(N/i) } else { C[l] += a[i] * brui[int(Nd/ld(i*l))]; } } for (ll j = 1; j <= m; j++){ ll jl = j*l; ll r = Nd / ld(jl); // m < i <= n/j = r if (m >= r) continue; if (jl <= L){ C[l] += b[j] * (A[jl] - arui[m]); // A[i] = A(N/i) } else { C[l] += b[j] * (arui[r] - arui[m]); } } } return make_pair(c,C); } // proposition 5 template pair,vector> divide_sparce(ll N, vector &a, vector &c, vector &A, vector &C){ ll K = a.size()-1, L = A.size()-1; // N <= K * L , K >= floor_sqrt(N) vector b = c; for (int i = 1; i <= K; i++){ b[i] /= a[1]; for (int j = 2; i * j <= K; j++){ b[i*j] -= a[j] * b[i]; } } vector arui(K+1,0), brui(K+1,0); for (int i = 1; i <= K; i++){ arui[i] = arui[i-1] + a[i]; brui[i] = brui[i-1] + b[i]; } ld Nd = N; vector B = C; for (ll l = L; l >= 1; l--){ ll n = Nd / ld(l); ll m = floor_sqrt(n); for (ll j = 1; j <= m; j++){ ll jl = j*l; ll r = Nd / ld(jl); if (m >= r) continue; if (jl <= L){ B[l] -= b[j] * (A[jl] - arui[m]); } else { B[l] -= b[j] * (arui[r] - arui[m]); } } } for (ll l = L; l >= 1; l--){ ll n = Nd / ld(l); ll m = floor_sqrt(n); for (ll i = 2; i <= m; i++){ ll il = i*l; if (il <= L){ B[l] -= a[i] * B[il]; } else { B[l] -= a[i] * brui[int(Nd/ld(il))]; } } B[l] /= a[1]; } return make_pair(b,B); } // usage : Totient_Sum(N) template T Totient_Sum(ll N){ if (N <= 0){ return T(0); } if (N == 1){ return T(1); } ll K = max( ceill(powl(ld(N)/logl(N),ld(2)/ld(3))) , sqrtl(N) ); ll L = N / K + 1; vector a(K+1,0), c(K+1,0); for (ll n = 1; n <= K; n++){ a[n] = 1; c[n] = n; } vector A(L+1,0), C(L+1,0); for (ll n = 1; n <= L; n++){ T m = N / n; A[n] = m; C[n] = m * (m+1) / 2; } return divide_sparce(N,a,c,A,C).second[1]; } // prefix sum of mobius function // n <= K ( K >= floor(sqrt(N)) ) or n = floor(N/i) ( for some i <= L ) template struct prefix_mu{ ll N, K, L; vector b, brui, B; prefix_mu(ll _N) : N(_N) { init(); } T get(ll n){ if (N <= 0){ return mint(0); } if (n <= K){ return brui[n]; } return B[N/n]; } void init(){ if (N <= 0) return ; if (N == 1){ b = {0,1}; brui = {0,1}; B = {0,1}; return ; } K = max( ceill(powl(ld(N)/logl(N),ld(2)/ld(3))) , sqrtl(N) ); L = N / K + 1; vector a(K+1,1), c(K+1,0); a[0] = 0, c[1] = 1; vector A(L+1,0), C(L+1,1); C[0] = 0; for (ll n = 1; n <= L; n++){ ll m = N / n; A[n] = m; } auto bB = divide_sparce(N,a,c,A,C); b = bB.first, B = bB.second; brui.resize(K+1,0); for (ll n = 1; n <= K; n++){ brui[n] = brui[n-1] + b[n]; } } }; } // namespace noya2 /* random checker #include"dirichlet.hpp" #include"random_kyopro.hpp" void solve(){ int n = rnd(1,200000); vector a(n+1), b(n+1); //cin >> a >> b; for (int i = 1; i <= n; i++){ a[i] = rnd(10000); b[i] = rnd(10000); } vector c(n+1,0); for (int i = 1; i <= n; i++){ for (int j = 1; i * j <= n; j++){ c[i*j] += a[i] * b[j]; } } vector arui(n+1,0), brui(n+1,0), crui(n+1,0); rep(i,n){ arui[i+1] = arui[i] + a[i+1]; brui[i+1] = brui[i] + b[i+1]; crui[i+1] = crui[i] + c[i+1]; } int s = floor_sqrt(n); vector ap(s+1), bp(s+1); rep(i,s+1){ ap[i] = a[i]; bp[i] = b[i]; } int t = n/s+2; vector Ap(t+1), Bp(t+1); repp(i,t+1,1){ Ap[i] = arui[n/i]; Bp[i] = brui[n/i]; } auto [cp, Cp] = multiply_sparce(n,ap,bp,Ap,Bp); auto [bq, Bq] = divide_sparce(n,ap,cp,Ap,Cp); for (int i = 1; i <= s; i++){ assert(c[i] == cp[i]); } for (int i = 1; i <= t; i++){ assert(crui[n/i] == Cp[i]); } assert(bp == bq); assert(Bp == Bq); //out(a), out(b), out(arui), out(brui); //out(c), out(crui); //out(ap); out(Ap); //out(bp); out(Bp); //out(cp); out(Cp); //out(bq); out(Bq); } */ #line 79 "c.cpp" void solve(){ int n, m; cin >> n >> m; const int mx = 30002; vector a(mx,0), b(mx,0); rep(i,n){ int x; cin >> x; a[x] = 1; } rep(j,m){ int y; cin >> y; b[y] = 1; } if (a[1] == 0 || b[1] == 0){ out(1); return ; } int z = 1; while (a[z] == 1 || b[z] == 1) z++; Dirichlet dir(mx); auto fast_divisor_enumeration = [&](int N){ vector

pes; for (int p : dir.primes){ int e = 0; while (N % p == 0){ N /= p; e++; } if (e > 0) pes.emplace_back(p,e); } if (N != 1) pes.emplace_back(N,1); vector res = {1}; for (auto pe : pes){ vector nres; for (auto x : res){ for (int _t = 0; _t <= pe.second; _t++){ nres.emplace_back(x); x *= pe.first; } } swap(res,nres); } return res; }; for (int x = z*z; x < (z+1)*(z+1); x++){ bool ok = false; for (int p : fast_divisor_enumeration(x)){ int q = x / p; int sp = sqrt_safe(p); int sq = sqrt_safe(q); if (a[sp] == 1 && b[sq] == 1) ok = true; } if (ok) continue; out(x); break; } } int main(){ fast_io(); int t = 1; //cin >> t; while(t--) solve(); }