結果
| 問題 | No.2497 GCD of LCMs |
| ユーザー |
 dyktr_06
|
| 提出日時 | 2023-10-06 22:43:13 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 218 ms / 2,000 ms |
| コード長 | 11,578 bytes |
| コンパイル時間 | 26,389 ms |
| コンパイル使用メモリ | 359,976 KB |
| 最終ジャッジ日時 | 2025-02-17 05:22:55 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 14 |
ソースコード
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) a.begin(), a.end()
#define Sort(a) sort(a.begin(), a.end())
#define RSort(a) sort(a.rbegin(), a.rend())
typedef long long int ll;
typedef unsigned long long ul;
typedef long double ld;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef vector<char> vc;
typedef vector<string> vst;
typedef vector<double> vd;
typedef vector<long double> vld;
typedef pair<long long, long long> P;
template<class T> long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T& a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T& a){ return *max_element(a.begin(), a.end()); }
const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }
template<class T, class U> inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T, class U> void inGraph(vector<vector<T>>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } }
namespace prime{
template <typename T>
bool isPrime(T n){
switch(n) {
case 0: // fall-through
case 1: return false;
case 2: return true;
}
if(n % 2 == 0) return false;
for(T i = 3; i*i <= n; i += 2){
if(n % i == 0){
return false;
}
}
return true;
}
template <typename T>
vector<pair<T, T>> factorize(T n) {
vector<pair<T, T>> ret;
for (T i = 2; i * i <= n; i++) {
if (n % i != 0) continue;
T tmp = 0;
while (n % i == 0) {
tmp++;
n /= i;
}
ret.push_back(make_pair(i, tmp));
}
if (n != 1) ret.push_back(make_pair(n, 1));
return ret;
}
template <typename T>
vector<T> divisor(T n){
T rt = sqrt(n);
vector<T> res, resB;
for(T i = 1; i * i <= n; i++){
if(n % i == 0){
res.push_back(i);
T j = n / i;
if(j != rt){
resB.push_back(j);
}
}
}
for(int i = (int) resB.size() - 1; i >= 0; i--){
res.push_back(resB[i]);
}
return res;
}
template <typename T>
vector<T> sieve(T n){
vector<T> c(n+1);
for(int i = 2; i <= n; i++){
if(c[i] != 0) continue;
for(int j = i; j <= n; j += i){
c[j] += 1;
}
}
return c;
}
}
namespace modcalc{
template <typename T>
T modpow(T x, T n, const T &m){
T ret = 1 % m;
x %= m;
while(n > 0){
if(n & 1) (ret *= x) %= m;
(x *= x) %= m;
n >>= 1;
}
return ret;
}
template <typename T>
T modinv(T a, T m){
T b = m, u = 1, v = 0;
while(b){
T t = a / b;
a -= t * b; swap(a, b);
u -= t * v; swap(u, v);
}
u %= m;
if (u < 0) u += m;
return u;
}
template <typename T>
T modarithmeticsum(T a, T d, T n, T m){
T m2 = m * 2;
a %= m2, n %= m2, d %= m2;
T b = (n - 1) * d % m2;
return ((n * (a * 2 + b) % m2) / 2) % m;
}
template <typename T>
T modgeometricsum(T a, T r, T n, T m){
a %= m;
if(r == 1){
n %= m;
return a * n % m;
}
return a * (modpow(r, n, m) + m - 1) % m * modinv(r - 1, m) % m;
}
template <typename T>
T modgeometricsum2(T a, T r, T n, T m){
a %= m;
if(r == 1){
n %= m;
return a * n % m;
}
T ret = 0;
T x = 1 % m;
T sum = 0;
for(int i = 0; n > 0; ++i){
if(n & 1){
(ret += x * modpow(r, sum, m) % m) %= m;
sum |= 1LL << i;
}
(x += x * modpow(r, 1LL << i, m) % m) %= m;
n >>= 1;
}
return a * ret % m;
}
}
template <long long Modulus>
struct ModInt{
long long val;
constexpr ModInt(const long long &_val = 0) noexcept : val(_val) {
normalize();
}
void normalize(){
val = (val % Modulus + Modulus) % Modulus;
}
inline ModInt& operator+=(const ModInt& rhs) noexcept {
if(val += rhs.val, val >= Modulus) val -= Modulus;
return *this;
}
inline ModInt& operator-=(const ModInt& rhs) noexcept {
if(val -= rhs.val, val < 0) val += Modulus;
return *this;
}
inline ModInt& operator*=(const ModInt& rhs) noexcept {
val = val * rhs.val % Modulus;
return *this;
}
inline ModInt& operator/=(const ModInt& rhs) noexcept {
val = val * inv(rhs.val).val % Modulus;
return *this;
}
inline ModInt& operator++() noexcept {
if(++val >= Modulus) val -= Modulus;
return *this;
}
inline ModInt operator++(int) noexcept {
ModInt t = val;
if(++val >= Modulus) val -= Modulus;
return t;
}
inline ModInt& operator--() noexcept {
if(--val < 0) val += Modulus;
return *this;
}
inline ModInt operator--(int) noexcept {
ModInt t = val;
if(--val < 0) val += Modulus;
return t;
}
inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
inline ModInt inv(void) const { return inv(val); }
ModInt inv(const long long& n) const {
long long a = n, b = Modulus, u = 1, v = 0;
while(b){
long long t = a / b;
a -= t * b; swap(a, b);
u -= t * v; swap(u, v);
}
u %= Modulus;
if(u < 0) u += Modulus;
return u;
}
friend inline ModInt operator+(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) += rhs; }
friend inline ModInt operator-(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) -= rhs; }
friend inline ModInt operator*(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) *= rhs; }
friend inline ModInt operator/(const ModInt& lhs, const ModInt& rhs) noexcept { return ModInt(lhs) /= rhs; }
friend inline bool operator==(const ModInt& lhs, const ModInt& rhs) noexcept { return lhs.val == rhs.val; }
friend inline bool operator!=(const ModInt& lhs, const ModInt& rhs) noexcept { return lhs.val != rhs.val; }
friend inline istream& operator>>(istream& is, ModInt& x) noexcept {
is >> x.val;
x.normalize();
return is;
}
friend inline ostream& operator<<(ostream& os, const ModInt& x) noexcept { return os << x.val; }
};
using mint = ModInt<998244353>;
template <typename T>
vector<long long> dijkstra(const vector<vector<array<long long, 2>>> &G, T x){
const long long INF = 0x1fffffffffffffff;
vector<long long> cost((int) G.size(), INF);
using P = pair<long long, long long>;
priority_queue<P, vector<P>, greater<>> q;
cost[x] = 0;
q.emplace(0, x);
while(q.size()){
auto [c, at] = q.top();
q.pop();
if(c > cost[at]) continue;
for(auto& [to, t] : G[at]){
if(cost[to] > max(c, t)){
cost[to] = max(c, t);
q.emplace(cost[to], to);
}
}
}
return cost;
}
ll n, m;
vll a;
vll u, v;
void input(){
in(n, m);
vin(a, n);
u.resize(m);
v.resize(m);
rep(i, m) in(u[i], v[i]);
}
void solve(){
rep(i, m) u[i]--, v[i]--;
map<ll, ll> mp;
vector<map<ll, ll>> p(n);
rep(i, n){
for(auto [x, y] : prime::factorize(a[i])) p[i][x] = y;
}
rep(i, n){
for(auto [x, y] : p[i]){
if(mp.count(x) == 0){
mp[x] = y;
}else{
chmax(mp[x], y);
}
}
}
vector<mint> ans(n, 1);
for(auto [k, x] : mp){
vector<vector<array<ll, 2>>> G(2 * n);
rep(i, m){
G[n + u[i]].push_back({v[i], 0});
G[n + v[i]].push_back({u[i], 0});
}
rep(i, n){
G[i].push_back({n + i, p[i][k]});
}
vll cost = dijkstra(G, 0);
rep(i, n){
ans[i] *= modcalc::modpow(k, cost[n + i], MOD);
}
}
vout(ans, "\n");
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(20);
input();
solve();
}