結果
| 問題 | No.2497 GCD of LCMs |
| ユーザー |
 ZrjaK
|
| 提出日時 | 2023-11-08 17:15:08 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 417 ms / 2,000 ms |
| コード長 | 25,714 bytes |
| コンパイル時間 | 7,336 ms |
| コンパイル使用メモリ | 353,516 KB |
| 実行使用メモリ | 8,448 KB |
| 最終ジャッジ日時 | 2024-09-25 23:44:08 |
| 合計ジャッジ時間 | 9,448 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 3 ms
5,376 KB |
| testcase_02 | AC | 3 ms
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | AC | 3 ms
5,376 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 20 ms
5,376 KB |
| testcase_08 | AC | 110 ms
5,376 KB |
| testcase_09 | AC | 127 ms
5,376 KB |
| testcase_10 | AC | 231 ms
8,320 KB |
| testcase_11 | AC | 83 ms
5,504 KB |
| testcase_12 | AC | 289 ms
6,528 KB |
| testcase_13 | AC | 388 ms
8,448 KB |
| testcase_14 | AC | 59 ms
7,936 KB |
| testcase_15 | AC | 40 ms
7,552 KB |
| testcase_16 | AC | 417 ms
8,320 KB |
ソースコード
#ifdef ONLINE_JUDGE
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#endif
#include <bits/stdc++.h>
#include <ext/rope>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/hash_policy.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/trie_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
using namespace std;
using namespace __gnu_cxx;
using namespace __gnu_pbds;
template <class T> using pbds_set = tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;
using Trie = trie<string, null_type, trie_string_access_traits<>, pat_trie_tag, trie_prefix_search_node_update>;
// template <class T> using heapq = __gnu_pbds::priority_queue<T, greater<T>, pairing_heap_tag>;
template <class T> using heapq = std::priority_queue<T, vector<T>, greater<T>>;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using ld = long double;
using ui = unsigned int;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vpii = vector<pii>;
using vpll = vector<pll>;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = std::priority_queue<T>;
template <class T>
using pqg = std::priority_queue<T, vector<T>, greater<T>>;
#define lb lower_bound
#define ub upper_bound
#define pb push_back
#define pf push_front
#define eb emplace_back
#define fi first
#define se second
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define rep1(n) for(int i = 0; i < n; ++i)
#define rep2(i, n) for(int i = 0; i < n; ++i)
#define rep3(i, a, b) for(int i = a; i < b; ++i)
#define rep4(i, a, b, c) for(int i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1) (__VA_ARGS__)
#define rrep1(n) for(int i = n; i--; )
#define rrep2(i, n) for(int i = n; i--; )
#define rrep3(i, a, b) for(int i = a; i > b; i--)
#define rrep4(i, a, b, c) for(int i = a; i > b; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1) (__VA_ARGS__)
#define each1(i, a) for(auto&& i : a)
#define each2(x, y, a) for(auto&& [x, y] : a)
#define each3(x, y, z, a) for(auto&& [x, y, z] : a)
#define each(...) overload4(__VA_ARGS__, each3, each2, each1) (__VA_ARGS__)
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1) (__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R) (__VA_ARGS__)
#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define len(x) (int)x.size()
#define elif else if
#define all1(i) begin(i), end(i)
#define all2(i, a) begin(i), begin(i) + a
#define all3(i, a, b) begin(i) + a, begin(i) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1) (__VA_ARGS__)
#define rall1(i) rbegin(i), rend(i)
#define rall2(i, a) rbegin(i), rbegin(i) + a
#define rall3(i, a, b) rbegin(i) + a, rbegin(i) + b
#define rall(...) overload3(__VA_ARGS__, rall3, rall2, rall1) (__VA_ARGS__)
#define mst(x, a) memset(x, a, sizeof(x))
#define bitcnt(x) (__builtin_popcountll(x))
#define endl "\n"
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
#define SORT(a) sort(all(a))
#define REV(a) reverse(all(a))
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template <typename T, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sum = 0;
for (auto &&a: A) sum += a;
return sum;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
for (int i = 0; i < N; i++) B[i + 1] = B[i] + A[i];
if (off == 0) B.erase(B.begin());
return B;
}
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
assert(!que.empty());
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
assert(!que.empty());
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
tie(ok, ng) = (check(x) ? make_pair(x, ng) : make_pair(ok, x));
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
while (iter--) {
double x = (ok + ng) / 2;
tie(ok, ng) = (check(x) ? make_pair(x, ng) : make_pair(ok, x));
}
return (ok + ng) / 2;
}
template <class T, class S> inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S> inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
mt19937 rng( chrono::steady_clock::now().time_since_epoch().count() );
#define Ran(a, b) rng() % ( (b) - (a) + 1 ) + (a)
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
size_t operator()(pair<uint64_t,uint64_t> x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x.first + FIXED_RANDOM) ^ (splitmix64(x.second + FIXED_RANDOM) >> 1);
}
};
const i128 ONE = 1;
istream &operator>>(istream &in, i128 &x) {
string s;
in >> s;
bool minus = false;
if (s[0] == '-') {
minus = true;
s.erase(s.begin());
}
x = 0;
for (auto i : s) {
x *= 10;
x += i - '0';
}
if (minus) x = -x;
return in;
}
ostream &operator<<(ostream &out, i128 x) {
string s;
bool minus = false;
if (x < 0) {
minus = true;
x = -x;
}
while (x) {
s.push_back(x % 10 + '0');
x /= 10;
}
if (s.empty()) s = "0";
if (minus) out << '-';
reverse(s.begin(), s.end());
out << s;
return out;
}
template <class T> ostream &operator<<(ostream &os, const set<T> &v) {
for(auto it = begin(v); it != end(v); ++it) {
if(it == begin(v)) os << *it;
else os << " " << *it;
}
return os;
}
template <class T> ostream &operator<<(ostream &os, const multiset<T> &v) {
for(auto it = begin(v); it != end(v); ++it) {
if(it == begin(v)) os << *it;
else os << " " << *it;
}
return os;
}
template <class T> ostream &operator<<(ostream &os, const pbds_set<T> &v) {
for(auto it = begin(v); it != end(v); ++it) {
if(it == begin(v)) os << *it;
else os << " " << *it;
}
return os;
}
template <class T, class S> istream &operator>>(istream &in, pair<T, S> &p) {
in >> p.first >> p.second;
return in;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
os << p.first << " " << p.second;
return os;
}
template <class T, size_t size> istream &operator>>(istream &in, array<T, size> &v) {
for(auto& x : v) in >> x;
return in;
}
template <class T, size_t size> ostream &operator<<(ostream &os, const array<T, size> &v) {
for(int i = 0; i < size; i++) {
if(i == 0) os << v[i];
else os << " " << v[i];
}
return os;
}
template <class T> istream &operator>>(istream &in, vector<T> &v) {
for(auto& x : v) in >> x;
return in;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
for(auto it = begin(v); it != end(v); ++it) {
if(it == begin(v)) os << *it;
else os << " " << *it;
}
return os;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head& head, const Tail &...tails) {
std::cout << head;
if (sizeof...(tails)) std::cout << ' ';
print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
for (auto it = v.begin(); it != v.end();) {
std::cout << *it;
if (++it != v.end()) std::cout << sep;
}
std::cout << end;
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
cin >> head;
read(tail...);
}
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
ll gcd(ll x, ll y) {
if(!x) return y;
if(!y) return x;
int t = __builtin_ctzll(x | y);
x >>= __builtin_ctzll(x);
do {
y >>= __builtin_ctzll(y);
if (x > y) swap(x, y);
y -= x;
} while (y);
return x << t;
}
ll lcm(ll x, ll y) { return x * y / gcd(x, y); }
ll exgcd(ll a, ll b, ll &x, ll &y) {
if(!b) return x = 1, y = 0, a;
ll d = exgcd(b, a % b, x, y);
ll t = x;
x = y;
y = t - a / b * x;
return d;
}
ll max(ll x, ll y) { return x > y ? x : y; }
ll min(ll x, ll y) { return x < y ? x : y; }
ll Mod(ll x, int mod) { return (x % mod + mod) % mod; }
ll pow(ll x, ll y, ll mod){
ll res = 1, cur = x;
while (y) {
if (y & 1) res = res * cur % mod;
cur = ONE * cur * cur % mod;
y >>= 1;
}
return res % mod;
}
ll probabilityMod(ll x, ll y, ll mod) {
return x * pow(y, mod-2, mod) % mod;
}
vvi getGraph(int n, int m, bool directed = false) {
vvi res(n);
rep(_, 0, m) {
int u, v;
cin >> u >> v;
u--, v--;
res[u].emplace_back(v);
if(!directed) res[v].emplace_back(u);
}
return res;
}
vector<vpii> getWeightedGraph(int n, int m, bool directed = false) {
vector<vpii> res(n);
rep(_, 0, m) {
int u, v, w;
cin >> u >> v >> w;
u--, v--;
res[u].emplace_back(v, w);
if(!directed) res[v].emplace_back(u, w);
}
return res;
}
template <class... Args> auto ndvector(size_t n, Args &&...args) {
if constexpr (sizeof...(args) == 1) {
return vector(n, args...);
} else {
return vector(n, ndvector(args...));
}
}
const ll LINF = 0x1fffffffffffffff;
const ll MINF = 0x7fffffffffff;
const int INF = 0x3fffffff;
const int MOD = 1000000007;
const int MODD = 998244353;
const int N = 1e6 + 10;
namespace SPRP {
// http://miller-rabin.appspot.com/
const std::vector<std::vector<__int128>> bases{
{126401071349994536}, // < 291831
{336781006125, 9639812373923155}, // < 1050535501 (1e9)
{2, 2570940, 211991001, 3749873356}, // < 47636622961201 (4e13)
{2, 325, 9375, 28178, 450775, 9780504, 1795265022} // <= 2^64
};
inline int get_id(long long n) {
if (n < 291831) {
return 0;
} else if (n < 1050535501) {
return 1;
} else if (n < 47636622961201)
return 2;
else { return 3; }
}
} // namespace SPRP
// Miller-Rabin primality test
// https://ja.wikipedia.org/wiki/%E3%83%9F%E3%83%A9%E3%83%BC%E2%80%93%E3%83%A9%E3%83%93%E3%83%B3%E7%B4%A0%E6%95%B0%E5%88%A4%E5%AE%9A%E6%B3%95
// Complexity: O(lg n) per query
struct {
long long modpow(__int128 x, __int128 n, long long mod) noexcept {
__int128 ret = 1;
for (x %= mod; n; x = x * x % mod, n >>= 1) ret = (n & 1) ? ret * x % mod : ret;
return ret;
}
bool operator()(long long n) noexcept {
if (n < 2) return false;
if (n % 2 == 0) return n == 2;
int s = __builtin_ctzll(n - 1);
for (__int128 a : SPRP::bases[SPRP::get_id(n)]) {
if (a % n == 0) continue;
a = modpow(a, (n - 1) >> s, n);
bool may_composite = true;
if (a == 1) continue;
for (int r = s; r--; a = a * a % n) {
if (a == n - 1) may_composite = false;
}
if (may_composite) return false;
}
return true;
}
} is_prime;
struct {
// Pollard's rho algorithm: find factor greater than 1
long long find_factor(long long n) {
assert(n > 1);
if (n % 2 == 0) return 2;
if (is_prime(n)) return n;
long long c = 1;
auto f = [&](__int128 x) -> long long { return (x * x + c) % n; };
for (int t = 1;; t++) {
for (c = 0; c == 0 or c + 2 == n;) c = rng() % n;
long long x0 = t, m = std::max(n >> 3, 1LL), x, ys, y = x0, r = 1, g, q = 1;
do {
x = y;
for (int i = r; i--;) y = f(y);
long long k = 0;
do {
ys = y;
for (int i = std::min(m, r - k); i--;)
y = f(y), q = __int128(q) * std::abs(x - y) % n;
g = std::__gcd<long long>(q, n);
k += m;
} while (k < r and g <= 1);
r <<= 1;
} while (g <= 1);
if (g == n) {
do {
ys = f(ys);
g = std::__gcd(std::abs(x - ys), n);
} while (g <= 1);
}
if (g != n) return g;
}
}
std::vector<long long> operator()(long long n) {
std::vector<long long> ret;
while (n > 1) {
long long f = find_factor(n);
if (f < n) {
auto tmp = operator()(f);
ret.insert(ret.end(), tmp.begin(), tmp.end());
} else
ret.push_back(n);
n /= f;
}
std::sort(ret.begin(), ret.end());
return ret;
}
long long euler_phi(long long n) {
long long ret = 1, last = -1;
for (auto p : this->operator()(n)) ret *= p - (last != p), last = p;
return ret;
}
} FactorizeLonglong;
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
else v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
friend const Type& abs(const Modular& x) { return x.value; }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename V, typename U>
friend V& operator>>(V& stream, Modular<U>& number);
private:
Type value;
};
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
return to_string(number());
}
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
return stream << number();
}
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, long long>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/
constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
Mint C(int n, int k) {
if (k < 0 || k > n) {
return 0;
}
while ((int) fact.size() < n + 1) {
fact.push_back(fact.back() * (int) fact.size());
inv_fact.push_back(1 / fact.back());
}
return fact[n] * inv_fact[k] * inv_fact[n - k];
}
void solve() {
INT(n, m);
VEC(int, a, n);
auto d = getGraph(n, m);
set<int> P;
vc<map<int, int>> primes;
each(x, a) {
map<int, int> M;
each(i, FactorizeLonglong(x)) P.insert(i), M[i]++;
primes.pb(M);
}
vc<Mint> ans(n, 1);
each(p, P) {
vc<ll> dist(n, infty<ll>);
dist[0] = primes[0][p];
set<pll> S = {{dist[0], 0}};
while (len(S)) {
auto [_, i] = *begin(S);
S.erase(begin(S));
each(j, d[i]) if (chmin(dist[j], max(dist[i], primes[j][p]))) {
S.insert({dist[j], j});
}
}
rep(i, n) ans[i] *= power(Mint(p), dist[i]);
}
print_all(ans, "\n");
}
signed main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cout << fixed << setprecision(15);
int t = 1;
// cin >> t;
while (t--) {
solve();
}
return 0;
}