結果
| 問題 |
No.2578 Jewelry Store
|
| コンテスト | |
| ユーザー |
 Nachia
|
| 提出日時 | 2023-12-06 01:03:13 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,278 ms / 3,500 ms |
| コード長 | 6,570 bytes |
| コンパイル時間 | 1,288 ms |
| コンパイル使用メモリ | 109,036 KB |
| 最終ジャッジ日時 | 2025-02-18 08:06:39 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 54 |
ソースコード
#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
#include <atcoder/modint>
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<(i64)(n); i++)
#define repr(i,n) for(i64 i=(i64)(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
template<typename A> using nega_queue = priority_queue<A,vector<A>,greater<A>>;
using Modint = atcoder::static_modint<998244353>;
//#include "nachia/vec.hpp"
namespace nachia{
int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
return __builtin_popcountll(c);
#else
c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
c = (c * (~0ull/257)) >> 56;
return c;
#endif
}
// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return 63 - __builtin_clzll(x);
#else
using u64 = unsigned long long;
int q = (n >> 32) ? 32 : 0;
auto m = n >> q;
constexpr u64 hi = 0x8888'8888;
constexpr u64 mi = 0x1111'1111;
m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
m = (((m | ~(hi - (n & ~hi))) & hi) * mi) >> 31;
q += (m & 0xf) << 2;
q += 0x3333'3333'2222'1100 >> (((n >> q) & 0xf) << 2) & 0xf
return q;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
return __builtin_ctzll(x);
#else
return MsbIndex(x & -x);
#endif
}
}
namespace nachia{
template<class Int> Int BinaryGcd(Int a, Int b){
if(a < 0) a = -a;
if(b < 0) b = -b;
if(!a || !b) return a|b;
int q = LsbIndex(a|b);
b >>= LsbIndex(b);
a >>= LsbIndex(a);
while(a!=b){
if(a<b){ b-=a; b>>=LsbIndex(b); }
else{ a-=b; a>>=LsbIndex(a); }
}
return a<<q;
}
}
#include <initializer_list>
namespace nachia{
bool IsPrime(unsigned long long x) noexcept {
if(x <= 1) return false;
if(x % 2 == 0) return x == 2;
using u64 = unsigned long long;
using u128 = __uint128_t;
u64 d = x-1;
int s = 0;
int q = 63;
while(!(d&1)){ d >>= 1; s++; }
while(!(d >> q)) q--;
u64 r = x; for(int t=0; t<6; t++) r*=2-r*x;
u128 n2 = -(u128)x % x;
auto red = [=](u128 t) noexcept -> u64 {
t = (t + (u128)((u64)t*-r)*x) >> 64;
return (t >= x) ? t-x : t;
};
u64 one = red(n2);
for(u64 base : { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }){
if(base%x==0) continue;
u64 a = base = red(base%x*n2);
for(int e=q-1; e>=0; e--){ a = red((u128)a*a); if((d>>e)&1) a = red((u128)a*base); }
if(a == one) continue;
for(int t=1; t<s&&a!=x-one; t++) a = red((u128)a*a);
if(a != x-one) return false;
}
return true;
}
} // namespace nachia
namespace nachia{
std::vector<std::pair<unsigned long long, int>> Factorize(unsigned long long x){
if(x == 1) return {};
if(IsPrime(x)) return {{x,1}};
using u64 = unsigned long long;
using u128 = __uint128_t;
u64 X = x;
std::vector<u64> p;
for(u64 i=2; i<100; i+=1+i%2) if(x%i==0){ p.push_back(i); while(x%i==0) x/=i; }
u64 r=1; u128 n2=1;
auto updX = [&](){
r = x; for(int t=0; t<6; t++) r*=2-r*x;
n2 = -(u128)x % x;
};
auto red = [&](u128 t) noexcept -> u64 {
u64 s = ((u128)x*((u64)t*r)) >> 64;
u64 t2 = t >> 64;
return t2-s + (t2 < s ? x : 0);
};
auto mult = [&](u64 a, u64 b) noexcept { return red((u128)red((u128)a*n2)*b); };
auto gcd = [](u64 a, u64 b) noexcept {
if(!a || !b) return a|b;
int q = LsbIndex(a|b);
b >>= LsbIndex(b);
a >>= LsbIndex(a);
while(a!=b){
if(a<b){ b-=a; b>>=LsbIndex(b); }
else{ a-=b; a>>=LsbIndex(a); }
}
return a<<q;
};
static u64 v = 7001;
p.push_back(x);
for(int pi=p.size()-1; pi<(int)p.size(); pi++) while(p[pi] != 1 && !IsPrime(p[pi])){
x = p[pi]; updX();
while(p[pi] == x){
v^=v<<13; v^=v>>7; v^=v<<17; // Xorshift https://www.jstatsoft.org/article/download/v008i14/916
u64 c = red(v); if(c == 0) continue;
auto f = [=](u64 a) noexcept -> u64 { return red((u128)a*a+c); };
u64 a=0, b=f(a);
u64 buf = 1, sz = 1, nx = 10;
while(true){
while(nx != sz && a != b){
buf = mult(buf, a<=b?b-a:a-b); sz++;
a = f(a); b = f(f(b));
}
u64 g = gcd(buf, x);
if(g != 1){
while(p[pi] % g == 0) p[pi] /= g;
p.push_back(g);
break;
}
if(a == b) break;
nx = sz * 3 / 2;
}
}
}
std::vector<std::pair<u64, int>> res;
for(u64 q : p) if(q != 1){
int e=0; while(X%q == 0){ e++; X/=q; }
if(e) res.push_back({ q, e });
}
return res;
}
unsigned long long Totient(unsigned long long x){
auto F = Factorize(x);
for(auto f : F) x -= x / f.first;
return x;
}
} // namespace nachia
void testcase(){
int T; cin >> T;
i64 M; cin >> M;
auto pf = nachia::Factorize(M);
int n = pf.size();
vector<i64> pes(n, 1);
rep(i,n) rep(j,pf[i].second) pes[i] *= pf[i].first;
rep(caseid, T){
int N; cin >> N;
vector<Modint> W(N);
{
int b,c,d; cin >> b >> c >> d;
W[0] = b;
rep(i,N-1) W[i+1] = W[i] * c + d;
}
vector<i64> A(N);
rep(i,N) cin >> A[i];
rep(i,N) if(M % A[i] != 0){ A[i] = 1; W[i] = 0; }
vector<Modint> F(1<<n, 1);
rep(i,N) if(W[i].val() != 0){
int q = 0;
rep(b,n) if(A[i] % pes[b] == 0) q += 1 << b;
F[q] *= W[i] + 1;
}
rep(d,n) rep(i,1<<n) if(i&(1<<d)) F[i] *= F[i-(1<<d)];
rep(d,n) rep(i,1<<n) if(i&(1<<d)) F[i] -= F[i-(1<<d)];
F[0] -= 1;
cout << F.back().val() << '\n';
}
}
int main(){
ios::sync_with_stdio(false); cin.tie(nullptr);
#ifdef NACHIA
int T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)
#endif
testcase();
return 0;
}