#846600 (C++17(gcc12)) No.2244 Integer Complete

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結果

問題	No.2244 Integer Complete
ユーザー	noya2
提出日時	2023-03-07 14:08:06
言語	C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
結果	AC
実行時間	10 ms / 2,000 ms
コード長	16,777 bytes
コンパイル時間	4,997 ms
コンパイル使用メモリ	280,828 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-09-18 02:27:11
合計ジャッジ時間	6,862 ms
ジャッジサーバーID （参考情報）	judge5 / judge2
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ファイルパターン	結果
other	AC * 60
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ソースコード

raw source code
#line 1 "c.cpp"
#include<bits/stdc++.h>
#include<atcoder/all>
#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<int, int>;
using PL = pair<long long, long long>;
using pdd = pair<long double, long double>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
template<class T>istream &operator>>(istream &is,vector<T> &v){for(auto &e:v)is>>e;return is;}
template<typename T>bool range(T a,T b,T x){return (a<=x&&x<b);}
template<typename T>bool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));}
template<typename T> T rev(const T& str_or_vec){T res = str_or_vec; reverse(res.begin(),res.end()); return res; }
template<typename T>bool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;}
template<typename T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<typename T>void uniq(vector<T> &v){sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}
template<typename T1, typename T2>void print(pair<T1,T2> a);
template<typename T>void print(vector<T> v);
template<typename T>void print(vector<vector<T>> 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<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template<typename T1,typename T2>void print(pair<T1,T2> a){print(a.first);print(),print(a.second);}
template<typename T>void print(vector<T> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}}
template<typename T>void print(vector<vector<T>> 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<<fixed<<setprecision(20);}
void o(){out("!?");}

namespace noya2{

const int INF = 1001001007;
const long long mod1 = 998244353;
const long long mod2 = 1000000007;
const long long inf = 2e18;
const long double pi = 3.14159265358979323;
const long double eps = 1e-7;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> 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<mint> a){vector<ll> b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);}
void out(vector<vector<mint>> a){for (auto v : a) out(v);}
istream &operator>>(istream &is,vector<mint> &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<typename T> 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<ll,ll> 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<ll,ll> res = ext_gcd(a,b,-c);
        res.first = -res.first, res.second = -res.second;
        return res;
    }
    if (c == 0) return pair<ll,ll>(0,0);
    if (a == 0 && b == 0) return pair<ll,ll>(0,0); // answer not exist
    ll g = gcd_safe(a,b);
    if (c % g != 0) return pair<ll,ll>(0,0); // answer not exist
    a /= g, b /= g, c /= g;
    ll x, y;
    if (b == 0) return pair<ll,ll>(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<ll,ll>(x,y);
}

template<typename T>
T ceil_safe(T p, T q);

template<typename T>
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<typename T>
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<int> 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;
            }
        }
    }
};
vector<int>Eratosthenes::table = vector<int>(0);

void build_eratosthenes(const int Nmax){Eratosthenes::init(Nmax);}

vector<pair<int,int>> fast_prime_factorization(int N){
    int pre = -1, cnt = 0;
    vector<pair<int,int>> 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<int> fast_divisor_enumeration(int N){
    auto pes = fast_prime_factorization(N);
    vector<int> res = {1};
    for (auto pe : pes){
        vector<int> 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<int> mobius(int N){
    vector<int> 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<pair<ll,int>> prime_factorization(ll N){
    vector<pair<ll,int>> 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<ll> divisor_enumeration(ll N){
    vector<ll> 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<int> 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<typename T> 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<typename T>
pair<vector<T>,vector<T>> multiply_sparce(ll N, vector<T> &a, vector<T> &b, vector<T> &A, vector<T> &B){
    ll K = a.size()-1, L = A.size()-1; // N <= K * L , K >= floor_sqrt(N)
    vector<T> 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<T> 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<T> 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<typename T>
pair<vector<T>,vector<T>> divide_sparce(ll N, vector<T> &a, vector<T> &c, vector<T> &A, vector<T> &C){
    ll K = a.size()-1, L = A.size()-1; // N <= K * L , K >= floor_sqrt(N)
    vector<T> 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<T> 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<T> 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<mint>(N) 
template<typename T>
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<T> a(K+1,0), c(K+1,0);
    for (ll n = 1; n <= K; n++){
        a[n] = 1;
        c[n] = n;
    }
    vector<T> 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<typename T>
struct prefix_mu{
    ll N, K, L;
    vector<T> 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<T> a(K+1,1), c(K+1,0);
        a[0] = 0, c[1] = 1;
        vector<T> 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<ll> 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<ll> 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<ll> 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<ll> ap(s+1), bp(s+1);
    rep(i,s+1){
        ap[i] = a[i];
        bp[i] = b[i];
    }
    int t = n/s+2;
    vector<ll> 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<int> 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<P> 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<int> res = {1};
        for (auto pe : pes){
            vector<int> 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();
}
yukicoder

結果

ソースコード
