#1195969 (C++23) No.2578 Jewelry Store

• 問題: No.2578 Jewelry Store
• ユーザー: apricity
• 提出日時: 2026-10-30 18:00:43
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 639 ms / 3,500 ms
• コード長: 18,694 bytes
• コンパイル時間: 2,027 ms
• コンパイル使用メモリ: 290,812 KB
• 実行使用メモリ: 9,908 KB
• 最終ジャッジ日時: 2026-10-30 18:01:00
• 合計ジャッジ時間: 15,156 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge1_0

ファイルパターン	結果
other	AC * 56

ソースコード

#ifdef LOCAL
#include "template.hpp"
#else
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<array>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<set>
#include<unordered_map>
#include<unordered_set>
#include<queue>
#include<stack>
#include<deque>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#include<functional>

using namespace std;

namespace io {

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
    for (auto &x : v) is >> x;
    return is;
}
template <typename T, size_t N = 0>
istream &operator>>(istream &is, array<T, N> &v) {
    for (auto &x : v) is >> x;
    return is;
}
template <size_t N = 0, typename T>
istream& cin_tuple_impl(istream &is, T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        is >> x;
        cin_tuple_impl<N + 1>(is, t);
    }
    return is;
}
template <class... T>
istream &operator>>(istream &is, tuple<T...> &t) {
    return cin_tuple_impl(is, t);
}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template<typename T, size_t N>
ostream &operator<<(ostream &os, const array<T, N> &v) {
    size_t n = v.size();
    for (size_t i = 0; i < n; i++) {
        if (i) os << " ";
        os << v[i];
    }
    return os;
}
template <size_t N = 0, typename T>
ostream& cout_tuple_impl(ostream &os, const T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) os << " ";
        const auto &x = std::get<N>(t);
        os << x;
        cout_tuple_impl<N + 1>(os, t);
    }
    return os;
}
template <class... T>
ostream &operator<<(ostream &os, const tuple<T...> &t) {
    return cout_tuple_impl(os, t);
}

void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
    cin >> t;
    in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
    cout << t;
    outr(u...);
}

void __attribute__((constructor)) _c() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);
}
} // namespace io

using io::in;
using io::out;
using io::outr;

#define SHOW(x) static_cast<void>(0)

using ll = long long;
using D = double;
using LD = long double;
using P = pair<ll, ll>;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = vector<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>>;
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;

#define rep1(a)          for(ll i = 0; i < a; i++)
#define rep2(i, a)       for(ll i = 0; i < a; i++)
#define rep3(i, a, b)    for(ll i = a; i < b; i++)
#define rep4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a)          for(ll i = (a)-1; i >= 0; i--)
#define rrep2(i, a)       for(ll i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b)    for(ll i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )
#define SZ(v) ll(v.size())
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(c, x) distance((c).begin(), lower_bound(ALL(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(ALL(c), (x)))
template <typename T, typename U>
T SUM(const vector<U> &v) {
    T res = 0;
    for(auto &&a : v) res += a;
    return res;
}
template <typename T>
vector<pair<T,int>> RLE(const vector<T> &v) {
    if (v.empty()) return {};
    T cur = v.front();
    int cnt = 1;
    vector<pair<T,int>> res;
    for (int i = 1; i < (int)v.size(); i++) {
        if (cur == v[i]) cnt++;
        else {
            res.emplace_back(cur, cnt);
            cnt = 1; cur = v[i];
        }
    }
    res.emplace_back(cur, cnt);
    return res;
}
template<class T, class S>
inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); }
template<class T, class S>
inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); }
void YESNO(bool flag) { out(flag ? "YES" : "NO"); }
void yesno(bool flag) { out(flag ? "Yes" : "No"); }

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); }
int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityl(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityl(x) & 1 ? -1 : 1); }
int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
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 <typename T>
T get_bit(T x, int k) { return x >> k & 1; }
template <typename T>
T set_bit(T x, int k) { return x | T(1) << k; }
template <typename T>
T reset_bit(T x, int k) { return x & ~(T(1) << k); }
template <typename T>
T flip_bit(T x, int k) { return x ^ T(1) << k; }

template <typename T>
T popf(deque<T> &que) { T a = que.front(); que.pop_front(); return a; }
template <typename T>
T popb(deque<T> &que) { T a = que.back(); que.pop_back(); return a; }
template <typename T>
T pop(queue<T> &que) { T a = que.front(); que.pop(); return a; }
template <typename T>
T pop(stack<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(PQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(minPQ<T> &que) { T a = que.top(); que.pop(); 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) {
        ll mid = (ok + ng) / 2;
        (check(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 60) {
    for (int _ = 0; _ < iter; _++) {
        double mid = (ok + ng) / 2;
        (check(mid) ? ok : ng) = mid;
    }
    return (ok + ng) / 2;
}

// max x s.t. b*x <= a
ll div_floor(ll a, ll b) {
    assert(b != 0);
    if (b < 0) a = -a, b = -b;
    return a / b - (a % b < 0);
}
// max x s.t. b*x < a
ll div_under(ll a, ll b) {
    assert(b != 0);
    if (b < 0) a = -a, b = -b;
    return a / b - (a % b <= 0);
}
// min x s.t. b*x >= a
ll div_ceil(ll a, ll b) {
    assert(b != 0);
    if (b < 0) a = -a, b = -b;
    return a / b + (a % b > 0);
}
// min x s.t. b*x > a
ll div_over(ll a, ll b) {
    assert(b != 0);
    if (b < 0) a = -a, b = -b;
    return a / b + (a % b >= 0);
}
// x = a mod b (b > 0), 0 <= x < b
ll modulo(ll a, ll b) {
    assert(b > 0);
    ll c = a % b;
    return c < 0 ? c + b : c;
}
// (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0)
// div_floor(a,b), modulo(a,b)
pair<ll,ll> divmod(ll a, ll b) {
    ll q = div_floor(a,b);
    return {q, a - b*q};
}
#endif

struct LazyMontgomeryModInt64 {
    using mint = LazyMontgomeryModInt64;
    using i64 = int64_t;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    static u64 mod;
    static u64 r;
    static u64 n2;

    static u64 get_r() {
        u64 ret = mod;
        for (int i = 0; i < 5; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static void set_mod(u64 mod_) {
        assert(mod_ < (1LL << 62));
        assert((mod_ & 1) == 1);
        mod = mod_;
        r = get_r();
        assert(r * mod == 1);
        n2 = -u128(mod) % mod;
    }

    u64 a;

    LazyMontgomeryModInt64() : a(0) {}
    LazyMontgomeryModInt64(const int64_t &b)
    : a(reduce(u128(b % mod + mod) * n2)){};

    static u64 reduce(const u128 &b) {
        return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
    }

    mint &operator+=(const mint &b) {
        if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator-=(const mint &b) {
        if (i64(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator*=(const mint &b) {
        a = reduce(u128(a) * b.a);
        return *this;
    }

    mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    mint operator+(const mint &b) const { return mint(*this) += b; }
    mint operator-(const mint &b) const { return mint(*this) -= b; }
    mint operator*(const mint &b) const { return mint(*this) *= b; }
    mint operator/(const mint &b) const { return mint(*this) /= b; }
    bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    mint operator-() const { return mint() - mint(*this); }
    mint operator+() const { return mint(*this); }

    mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    mint inverse() const {
        assert(a != 0);
        return this->pow(mod-2);
    }

    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }

    friend istream &operator>>(istream &is, mint &b) {
        i64 t;
        is >> t;
        b = LazyMontgomeryModInt64(t);
        return (is);
    }

    u64 get() const {
        u64 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static u64 get_mod() { return mod; }
};

using m64 = LazyMontgomeryModInt64;
typename m64::u64 m64::mod, m64::r, m64::n2;

bool miller_rabin(ll n, const vector<ll> &witness) {
    m64::set_mod(n);
    int s = 0, t;
    ll d = n - 1;
    while (d % 2 == 0) d >>= 1, s++;
    for (ll a : witness) {
        if (n <= a) return true;
        m64 x = m64(a).pow(d);
        if (x != 1) {
            for (t = 0; t < s; t++) {
                if (x == n-1) break;
                x = x * x;
            }
            if (t == s) return false;
        }
    }
    return true;
}

bool primality_test(ll n) {
    if (n <= 1) return false;
    if (n <= 2) return true;
    if (n % 2 == 0) return false;
    if (n < 4759123141LL) return miller_rabin(n, {2, 7, 61});
    else return miller_rabin(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

ll random_prime(ll lb, ll ub) {
    mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
    uniform_int_distribution<ll> rand(lb, ub);
    ll q;
    while (!primality_test(q = rand(mt)));
    return q;
}

ll pollard_rho(ll n) {
    if (n % 2 == 0) return 2;

    mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
    uniform_int_distribution<uint64_t> rand(0, n-1);
    m64::set_mod(n);
    static constexpr int m = 128;

    m64 c, one = 1;
    auto f = [&] (m64 x) -> m64 { return x * x + c; };

    m64 x, y, ys, q;
    int k, r;
    ll g;

    while (1) {
        c = rand(mt);
        y = 0;
        g = r = 1;
        q = one;
        k = 0;
        for (r = 1; g == 1; r <<= 1) {
            x = y;
            for (k = 0; k < 3 * r / 4; k++) y = f(y);
            for (; k < r and g == 1; k += m) {
                ys = y;
                for (int i = 0; i < m and i < r - k; i++) {
                    y = f(y);
                    q *= x - y;
                }
                g = gcd(q.get(), n);
            }
            k = r;
        }
        if (g == n) {
            g = 1;
            do {
                ys = f(ys);
                g = gcd((x - ys).get(), n);
            } while (g == 1);
        }
        if (g == n) continue;
        if (primality_test(g)) return g;
        else if (primality_test(n / g)) return n / g;
        else return pollard_rho(g);
    }
}

vector<pair<ll, int>> factorize(ll n) {
    vector<pair<ll, int>> res;
    while (n > 1 and !primality_test(n)) {
        ll p = pollard_rho(n);
        assert(primality_test(p));
        assert(n % p == 0);
        int e = 0;
        while (n % p == 0) {
            n /= p;
            e++;
        }
        res.emplace_back(p, e);
    }
    if (n > 1) res.emplace_back(n, 1);
    return res;
}

vector<ll> divisor(ll n) {
    vector<ll> res{1};
    const auto pf = factorize(n);
    for (const auto& [p, e] : pf) {
        int s = res.size();
        for (int i = 0; i < s; i++) {
            ll m = 1;
            for (int _ = 0; _ < e; _++) {
                m *= p;
                res.push_back(res[i]*m);
            }
        }
    }
    return res;
}

template <uint32_t mod>
struct LazyMontgomeryModInt {
    using mint = LazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static constexpr u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static constexpr u32 r = get_r();
    static constexpr u32 n2 = -u64(mod) % mod;
    static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
    static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
    static_assert(r * mod == 1, "this code has bugs.");

    u32 a;

    constexpr LazyMontgomeryModInt() : a(0) {}
    constexpr LazyMontgomeryModInt(const int64_t &b)
    : a(reduce(u64(b % mod + mod) * n2)){};

    static constexpr u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }

    constexpr mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }

    constexpr mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
    constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
    constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
    constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
    constexpr bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr mint operator-() const { return mint() - mint(*this); }
    constexpr mint operator+() const { return mint(*this); }

    constexpr mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    constexpr mint inverse() const {
        int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
        while (y > 0) {
            t = x / y;
            x -= t * y, u -= t * v;
            tmp = x, x = y, y = tmp;
            tmp = u, u = v, v = tmp;
        }
        return mint{u};
    }

    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }

    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = LazyMontgomeryModInt<mod>(t);
        return (is);
    }

    constexpr u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static constexpr u32 get_mod() { return mod; }
};
const int mod = 998244353;
//const int mod = 1000000007;
using mint = LazyMontgomeryModInt<mod>;

// b[s] = \sum_{t ⊇ s} a[t]
template <typename T>
void superset_zeta(vector<T> &a) {
    int n = a.size();
    assert((n & (n-1)) == 0);
    for (int i = 1; i < n; i <<= 1) {
        for (int s = 0; s < n; s++) {
            if (!(s & i)) a[s] *= a[s ^ i];
        }
    }
}
vector<pair<ll,int>> pf;
ll m;

void solve() {
    int n,b,c,d; in(n,b,c,d);
    vc<ll> a(n); in(a);
    vc<mint> w(n); w[0] = b;
    rep(i,1,n) w[i] = w[i-1] * c + d;
    int k = pf.size();
    vc<mint> pr(1<<k,1);
    rep(i,n){
        if(m%a[i]!=0) continue;
        int s = 0;
        rep(j,k){
            ll p = pf[j].first;
            if((m/p)%a[i] == 0) s |= 1<<j;
        }
        pr[s] *= w[i]+1;
    }
    superset_zeta(pr);
    mint ans = 0;
    rep(i,1<<k) ans += pr[i] * popcnt_sgn(i);
    if(m==1) ans -= 1;
    out(ans);
}

int main() {
    int tc = 1;
    in(tc);
    in(m);
    pf = factorize(m);
    while(tc--){
        solve();
    }
}