結果
| 問題 |
No.2578 Jewelry Store
|
| コンテスト | |
| ユーザー |
 Kude
|
| 提出日時 | 2023-12-06 02:16:07 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 944 ms / 3,500 ms |
| コード長 | 6,130 bytes |
| コンパイル時間 | 4,063 ms |
| コンパイル使用メモリ | 284,948 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-09-27 00:58:25 |
| 合計ジャッジ時間 | 12,663 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 54 |
ソースコード
#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
// https://ei1333.github.io/library/math/number-theory/fast-prime-factorization.hpp
namespace FastPrimeFactorization {
template< typename word, typename dword, typename sword >
struct UnsafeMod {
UnsafeMod() : x(0) {}
UnsafeMod(word _x) : x(init(_x)) {}
bool operator==(const UnsafeMod &rhs) const {
return x == rhs.x;
}
bool operator!=(const UnsafeMod &rhs) const {
return x != rhs.x;
}
UnsafeMod &operator+=(const UnsafeMod &rhs) {
if((x += rhs.x) >= mod) x -= mod;
return *this;
}
UnsafeMod &operator-=(const UnsafeMod &rhs) {
if(sword(x -= rhs.x) < 0) x += mod;
return *this;
}
UnsafeMod &operator*=(const UnsafeMod &rhs) {
x = reduce(dword(x) * rhs.x);
return *this;
}
UnsafeMod operator+(const UnsafeMod &rhs) const {
return UnsafeMod(*this) += rhs;
}
UnsafeMod operator-(const UnsafeMod &rhs) const {
return UnsafeMod(*this) -= rhs;
}
UnsafeMod operator*(const UnsafeMod &rhs) const {
return UnsafeMod(*this) *= rhs;
}
UnsafeMod pow(uint64_t e) const {
UnsafeMod ret(1);
for(UnsafeMod base = *this; e; e >>= 1, base *= base) {
if(e & 1) ret *= base;
}
return ret;
}
word get() const {
return reduce(x);
}
static constexpr int word_bits = sizeof(word) * 8;
static word modulus() {
return mod;
}
static word init(word w) {
return reduce(dword(w) * r2);
}
static void set_mod(word m) {
mod = m;
inv = mul_inv(mod);
r2 = -dword(mod) % mod;
}
static word reduce(dword x) {
word y = word(x >> word_bits) - word((dword(word(x) * inv) * mod) >> word_bits);
return sword(y) < 0 ? y + mod : y;
}
static word mul_inv(word n, int e = 6, word x = 1) {
return !e ? x : mul_inv(n, e - 1, x * (2 - x * n));
}
static word mod, inv, r2;
word x;
};
using uint128_t = __uint128_t;
using Mod64 = UnsafeMod< uint64_t, uint128_t, int64_t >;
template<> uint64_t Mod64::mod = 0;
template<> uint64_t Mod64::inv = 0;
template<> uint64_t Mod64::r2 = 0;
using Mod32 = UnsafeMod< uint32_t, uint64_t, int32_t >;
template<> uint32_t Mod32::mod = 0;
template<> uint32_t Mod32::inv = 0;
template<> uint32_t Mod32::r2 = 0;
bool miller_rabin_primality_test_uint64(uint64_t n) {
Mod64::set_mod(n);
uint64_t d = n - 1;
while(d % 2 == 0) d /= 2;
Mod64 e{1}, rev{n - 1};
// http://miller-rabin.appspot.com/ < 2^64
for(uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
if(n <= a) break;
uint64_t t = d;
Mod64 y = Mod64(a).pow(t);
while(t != n - 1 && y != e && y != rev) {
y *= y;
t *= 2;
}
if(y != rev && t % 2 == 0) return false;
}
return true;
}
bool miller_rabin_primality_test_uint32(uint32_t n) {
Mod32::set_mod(n);
uint32_t d = n - 1;
while(d % 2 == 0) d /= 2;
Mod32 e{1}, rev{n - 1};
for(uint32_t a : {2, 7, 61}) {
if(n <= a) break;
uint32_t t = d;
Mod32 y = Mod32(a).pow(t);
while(t != n - 1 && y != e && y != rev) {
y *= y;
t *= 2;
}
if(y != rev && t % 2 == 0) return false;
}
return true;
}
bool is_prime(uint64_t n) {
if(n == 2) return true;
if(n == 1 || n % 2 == 0) return false;
if(n < uint64_t(1) << 31) return miller_rabin_primality_test_uint32(n);
return miller_rabin_primality_test_uint64(n);
}
uint64_t pollard_rho(uint64_t n) {
if(is_prime(n)) return n;
if(n % 2 == 0) return 2;
Mod64::set_mod(n);
uint64_t d;
Mod64 one{1};
for(Mod64 c{one};; c += one) {
Mod64 x{2}, y{2};
do {
x = x * x + c;
y = y * y + c;
y = y * y + c;
d = __gcd((x - y).get(), n);
} while(d == 1);
if(d < n) return d;
}
assert(0);
}
vector< uint64_t > prime_factor(uint64_t n) {
if(n <= 1) return {};
uint64_t p = pollard_rho(n);
if(p == n) return {p};
auto l = prime_factor(p);
auto r = prime_factor(n / p);
copy(begin(r), end(r), back_inserter(l));
return l;
}
};
} int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int tt;
ll m;
cin >> tt >> m;
auto pfs_vec = FastPrimeFactorization::prime_factor(m);
sort(all(pfs_vec));
vector<pair<ll, int>> fs;
for (ll p : pfs_vec) {
if (!fs.empty() && fs.back().first == p) fs.back().second++;
else fs.emplace_back(p, 1);
}
int sz = fs.size();
while (tt--) {
int n, b, c, d;
cin >> n >> b >> c >> d;
using mint = modint998244353;
vector<mint> cnt(1 << sz, 1);
rep(_, n) {
ll a;
cin >> a;
int idx = 0;
bool ok = true;
rep(i, sz) {
int c = 0;
while (a % fs[i].first == 0) {
a /= fs[i].first;
c++;
}
if (c > fs[i].second) {
ok = false;
break;
}
idx |= ll(c < fs[i].second) << i;
}
if (ok && a == 1) {
cnt[idx] *= b + 1;
}
b = ((ll)c * b + d) % mint::mod();
}
rep(k, sz) rep(s, 1 << sz) if (s >> k & 1) {
cnt[s ^ 1 << k] *= cnt[s];
}
mint ans;
rep(s, 1 << sz) {
mint v = cnt[s];
ans += __builtin_parity(s) ? -v : v;
}
if (m == 1) ans--;
cout << ans.val() << '\n';
}
}