#936967 (C++17) No.2578 Jewelry Store

• 問題: No.2578 Jewelry Store
• ユーザー: heno239
• 提出日時: 2023-12-06 23:30:38
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 1,001 ms / 3,500 ms
• コード長: 10,768 bytes
• コンパイル時間: 2,784 ms
• コンパイル使用メモリ: 168,100 KB
• 最終ジャッジ日時: 2025-02-18 08:49:43
• ジャッジサーバーID （参考情報）: judge2 / judge1

ファイルパターン	結果
other	AC * 54

ソースコード

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//ll mod = 1;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const int mod17 = 1000000007;
const ll INF = (ll)mod17 * mod17;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

using ld = double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

template<typename T>
void chmin(T& a, T b) {
    a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
    a = max(a, b);
}
template<typename T>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
    vector<T> res;
    int ida = 0, idb = 0;
    while (ida < a.size() || idb < b.size()) {
        if (idb == b.size()) {
            res.push_back(a[ida]); ida++;
        }
        else if (ida == a.size()) {
            res.push_back(b[idb]); idb++;
        }
        else {
            if (a[ida] < b[idb]) {
                res.push_back(a[ida]); ida++;
            }
            else {
                res.push_back(b[idb]); idb++;
            }
        }
    }
    return res;
}
template<typename T>
void cinarray(vector<T>& v) {
    rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
    rep(i, v.size()) {
        if (i > 0)cout << " "; cout << v[i];
    }
    cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
    if (n < 0) {
        ll res = mod_pow(x, -n, m);
        return mod_pow(res, m - 2, m);
    }
    if (abs(x) >= m)x %= m;
    if (x < 0)x += m;
    //if (x == 0)return 0;
    ll res = 1;
    while (n) {
        if (n & 1)res = res * x % m;
        x = x * x % m; n >>= 1;
    }
    return res;
}
//mod should be <2^31
struct modint {
    int n;
    modint() :n(0) { ; }
    modint(ll m) {
        if (m < 0 || mod <= m) {
            m %= mod; if (m < 0)m += mod;
        }
        n = m;
    }
    operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
    if (n == 0)return modint(1);
    modint res = (a * a) ^ (n / 2);
    if (n % 2)res = res * a;
    return res;
}

ll inv(ll a, ll p) {
    return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
    fact[0] = modint(1);
    for (int i = 0; i < max_n - 1; i++) {
        fact[i + 1] = fact[i] * modint(i + 1);
    }
    factinv[max_n - 1] = modint(1) / fact[max_n - 1];
    for (int i = max_n - 2; i >= 0; i--) {
        factinv[i] = factinv[i + 1] * modint(i + 1);
    }
}
modint comb(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
    a = abs(a); b = abs(b);
    if (a < b)swap(a, b);
    while (b) {
        ll r = a % b; a = b; b = r;
    }
    return a;
}
template<typename T>
void addv(vector<T>& v, int loc, T val) {
    if (loc >= v.size())v.resize(loc + 1, 0);
    v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
    fill(isp + 2, isp + mn, true);
    for (int i = 2; i < mn; i++) {
        if (!isp[i])continue;
        ps.push_back(i);
        for (int j = 2 * i; j < mn; j += i) {
            isp[j] = false;
        }
    }
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    if (res == st.begin())return st.end();
    res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
    return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
    a = a + b; return a;
}
mP operator-(mP a, mP b) {
    return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
    a = a - b; return a;
}
LP operator+(LP a, LP b) {
    return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
    a = a + b; return a;
}
LP operator-(LP a, LP b) {
    return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
    a = a - b; return a;
}
P operator-(P a, P b) {
    return { a.first - b.first,a.second - b.second };
}
P operator+(P a, P b) {
    return { a.first + b.first,a.second + b.second };
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
//int dx[4] = { 1,0,-1,0 };
//int dy[4] = { 0,1,0,-1 };

//------------------------------------

//https://manabitimes.jp/math/1192
//https://qiita.com/Kiri8128/items/eca965fe86ea5f4cbb98
//don't forget T=__int128
using T = __int128;

const int mn = 1000005;
bool isp[mn];
vector<int> ps;
void init() {
    fill(isp + 2, isp + mn, true);
    for (int i = 2; i < mn; i++) {
        if (!isp[i])continue;
        ps.push_back(i);
        for (int j = 2 * i; j < mn; j += i) {
            isp[j] = false;
        }
    }
}
ll safety_mod_pow(ll x, ll n, ll mod) {
    x %= mod;
    ll res = 1;
    while (n) {
        if (n & 1)res = (T)res * (T)x % (T)mod;
        n >>= 1; if (n == 0)break;
        x = (T)x * (T)x % (T)mod;
    }
    return res;
}

bool prime_test(ll p) {
    if (p == 1)return false;
    if (p < mn)return isp[p];
    if (p % 2 == 0)return false;
    int s = 0; ll d = p - 1;
    while (d % 2 == 0) {
        s++; d /= 2;
    }
    uniform_int_distribution<long long> ud(1, p - 1);
    rep(_, 10) {
        ll a = ud(mt);
        ll v = safety_mod_pow(a, d, p);
        if (v != 1) {
            bool exi = false;
            rep(i, s) {
                if (v == p - 1) {
                    exi = true; break;
                }
                if (i + 1 < s) {
                    v = (T)v * (T)v % (T)p;
                }
            }
            if (!exi)return false;
        }
    }
    return true;
}
ll find_prime(ll n) {
    assert(n > 1);
    uniform_int_distribution<ll> ud(1, n - 1);

    const int test_time = 10;
    const int block_size = 200;
    rep(tt, test_time) {
        ll c = ud(mt);
        vector<ll> x;
        x.push_back(ud(mt));

        vector<ll> ds;
        ll dpro = 1;
        for (int i = 1; i < block_size * block_size; i++) {
            while (x.size() <= 2 * i) {
                ll las = x.back();
                las = (T)las * (T)las % n;
                las += c;
                if (las >= n)las -= n;
                x.push_back(las);
            }
            ll d = abs(x[i] - x[2 * i]);
            ds.push_back(d);
            dpro = (T)dpro * (T)d % n;
            if (ds.size() == block_size) {
                ll g = gcd(dpro, n);
                if (1 < g) {
                    bool upd = false;
                    for (ll d : ds) {
                        ll g = gcd(d, n);
                        if (1 < g && g < n) {
                            if (prime_test(g))return g;
                            upd = true;
                            n = g;
                        }
                    }
                    if (!upd)break;
                }
                ds.clear();
                dpro = 1;
            }
        }
    }

    return n;
}

vector<LP> factor(ll n) {
    vector<LP> res;
    for (int p = 2; p < 100; p++) {
        if (p * p > n)break;
        if (n % p == 0) {
            int cnt = 0;
            while (n % p == 0) {
                n /= p; cnt++;
            }
            res.push_back({ p,cnt });
        }
    }
    while (n > 1) {
        ll p = find_prime(n);
        if (p < 0)break;
        int cnt = 0;
        while (n % p == 0) {
            n /= p; cnt++;
        }
        res.push_back({ p,cnt });
    }
    assert(n == 1);
    sort(all(res)); return res;
}


void solve() {
    int t; ll m; cin >> t >> m;
    auto ps = factor(m);
    int sz = ps.size();
    vector<int> cc(1 << sz);
    rep(i, (1 << sz))rep(j, sz)if (i & (1 << j))cc[i] ^= 1;
    if (sz % 2)rep(i, (1 << sz))cc[i] ^= 1;
    rep(_, t) {
        int n; ll b, c, d; cin >> n >> b >> c >> d;
        vector<ll> a(n);
        vector<modint> w(n);
        rep(i, n) {
            cin >> a[i];
            if (i == 0)w[i] = b;
            else w[i] = (modint)c * (w[i - 1]) + (modint)d;
        }
        vector<modint> val(1 << sz, 1);
        rep(i, n) {
            ll cop = a[i];
            int s = 0;
            rep(j, ps.size()) {
                ll p = ps[j].first;
                int c = 0;
                while (cop % p == 0 && c < ps[j].second) {
                    cop /= p; c++;
                }
                if (c == ps[j].second)s |= (1 << j);
            }
            if (cop > 1)continue;
            //cout << "? " << s << "\n";
            val[s] *= (modint)1 + w[i];
        }
        rep(j, sz) {
            rep(i, (1 << sz)) {
                if (i & (1 << j)) {
                    val[i] *= val[i ^ (1 << j)];
                }
            }
        }
        modint ans = 0;
        rep(i, (1 << sz)) {
            if (cc[i])ans -= val[i];
            else ans += val[i];
        }
        if (m == 1)ans -= 1;
        cout << ans << "\n";
    }
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    //cout << fixed<<setprecision(10);
    //init_f();
    init();
    //while(true)
    //expr();
    //int t; cin >> t; rep(i, t)
    solve();
    return 0;
}