#937141 (C++23) No.2578 Jewelry Store

• 問題: No.2578 Jewelry Store
• ユーザー: noya2
• 提出日時: 2023-12-07 20:06:23
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,096 ms / 3,500 ms
• コード長: 17,711 bytes
• コンパイル時間: 4,145 ms
• コンパイル使用メモリ: 268,736 KB
• 実行使用メモリ: 9,404 KB
• 最終ジャッジ日時: 2023-12-07 20:06:40
• 合計ジャッジ時間: 15,216 ms
• ジャッジサーバーID （参考情報）: judge11 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,676 KB
testcase_01	AC	3 ms; 6,676 KB
testcase_02	AC	11 ms; 6,676 KB
testcase_03	AC	9 ms; 6,676 KB
testcase_04	AC	24 ms; 6,676 KB
testcase_05	AC	10 ms; 6,676 KB
testcase_06	AC	11 ms; 6,676 KB
testcase_07	AC	23 ms; 6,676 KB
testcase_08	AC	9 ms; 6,676 KB
testcase_09	AC	24 ms; 6,676 KB
testcase_10	AC	43 ms; 6,676 KB
testcase_11	AC	9 ms; 6,676 KB
testcase_12	AC	7 ms; 6,676 KB
testcase_13	AC	7 ms; 6,676 KB
testcase_14	AC	7 ms; 6,676 KB
testcase_15	AC	7 ms; 6,676 KB
testcase_16	AC	41 ms; 6,676 KB
testcase_17	AC	24 ms; 6,676 KB
testcase_18	AC	6 ms; 6,676 KB
testcase_19	AC	15 ms; 6,676 KB
testcase_20	AC	23 ms; 6,676 KB
testcase_21	AC	23 ms; 6,676 KB
testcase_22	AC	10 ms; 6,676 KB
testcase_23	AC	15 ms; 6,676 KB
testcase_24	AC	9 ms; 6,676 KB
testcase_25	AC	11 ms; 6,676 KB
testcase_26	AC	9 ms; 6,676 KB
testcase_27	AC	244 ms; 6,676 KB
testcase_28	AC	346 ms; 6,676 KB
testcase_29	AC	352 ms; 6,676 KB
testcase_30	AC	386 ms; 6,676 KB
testcase_31	AC	256 ms; 6,676 KB
testcase_32	AC	163 ms; 6,784 KB
testcase_33	AC	210 ms; 6,676 KB
testcase_34	AC	268 ms; 6,676 KB
testcase_35	AC	67 ms; 6,676 KB
testcase_36	AC	223 ms; 7,392 KB
testcase_37	AC	116 ms; 6,676 KB
testcase_38	AC	142 ms; 6,676 KB
testcase_39	AC	128 ms; 6,676 KB
testcase_40	AC	142 ms; 6,676 KB
testcase_41	AC	131 ms; 6,676 KB
testcase_42	AC	116 ms; 6,676 KB
testcase_43	AC	179 ms; 6,676 KB
testcase_44	AC	98 ms; 6,676 KB
testcase_45	AC	154 ms; 6,676 KB
testcase_46	AC	127 ms; 6,676 KB
testcase_47	AC	658 ms; 6,676 KB
testcase_48	AC	359 ms; 9,404 KB
testcase_49	AC	1,096 ms; 6,676 KB
testcase_50	AC	957 ms; 6,676 KB
testcase_51	AC	114 ms; 6,676 KB
testcase_52	AC	432 ms; 6,676 KB
testcase_53	AC	47 ms; 6,676 KB

ソースコード

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

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>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

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...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(vector<T> &v){
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

namespace maroonrk {

//モンゴメリ乗算
//S=2^64, I=S^-1 mod N, R*N=-1 mod S, T=2^64 mod N, E=2^128 mod N
//re(x) (x<S*N) return (x*I)%N (+0 or N)
//(x*I) = (x/S) = (x+(x*R)%S*N)/S mod N
//mult(x,y) (x*y<S*N) return (x*y*I)%N (+0 or N)
//en(x) (x<S) モンゴメリ空間に移す
//de(x) (x<S*N) 元の空間に戻す
struct m64{
	using u128=__uint128_t;
	ull n,n2,r,t,e;
	m64(ull nn){
		n=nn;
        assert(n<(1ull<<61));//2^62 必要なときは factor で add を使う
        assert(n%2==1);
        n2=n*2;
        r=n&3;
        rep(_,5)r*=2-n*r;
        r=-r;
        assert(r*n==-1ull);
        t=-ull(n)%n;
        e=-u128(n)%n;
	}
	ull re(u128 x){return (x+u128(ull(x)*r)*n)>>64;}
	ull mult(ull x,ull y){return re(u128(x)*y);}
	ull en(ull x){return mult(x,e);}
	ull de(ull x){x=re(x);return x<n?x:x-n;}
	ull pow(ull x,ull p){
		ull res=t;
		while(p){
			if(p&1)res=mult(res,x);
			x=mult(x,x);
			p>>=1;
		}
		return res;
	}
	
	bool pri(){
		assert(n>=3);
		assert(n&1);
		ull d=n-1;
		int s=__builtin_ctzll(d);
		d>>=s;
		auto check=[&](ull a)-> int {
			a%=n;
			if(a==0)return 1;
			ull y=pow(en(a),d);
			if(de(y)==1||de(y)==n-1)return 0;
			rep(i,s){
				y=mult(y,y);
				if(de(y)==n-1)return 0;
			}
			return -1;
		};
		if(n<4759123141ull){
			for(ull a:{2, 7, 61}){
				int w=check(a);
				if(w)return w==1;
			}
		}else{
			for(ull a:{2, 325, 9375, 28178, 450775, 9780504, 1795265022}){
				int w=check(a);
				if(w)return w==1;
			}
		}
		return true;
	}
	
	ull c;
	ull f(ull x){return re(u128(x)*x+c);}
	ull div(){
		assert(n>=3);
		assert(n&1);
		if(pri())return n;
		mt19937_64 gen;
		while(1){
			c=gen()%(n-1)+1;
			ull y=gen()%(n-1)+1;
			for(ull s=1;;s<<=1){
				const ull x=n2-y;
				//const ull m=min(ull(1)<<max(signed(__lg(n))/3-9,0),s);
				const ull m=min(ull(1)<<(__lg(n)/5),s);
				rep(i,s/m){
					ull w=t,z=y;
					rep(j,m){
						y=f(y);
						w=mult(w,y+x);
						//w=mult(w,add(y,x)); (2^61<=n<2^62)
					}
					ull g=gcd(de(w),n);
					if(g!=1){
						if(g<n)return g;
						rep(j,m){
							z=f(z);
							if((g=gcd(de(z+x),n))!=1){
								if(g<n)return g;
								else goto fail;
							}
						}
						assert(false);
					}
				}
			}
			fail:;
		}
	}
};

bool isprime(ull n) {
	if(n<=1)return false;
	if(n==2)return true;
	if(n%2==0)return false;
	return m64(n).pri();
}

ull finddivisor(ull n){
	assert(n>1);
	if(n%2==0)return 2;
	return m64(n).div();
}

vector<ull> factorize(ull n){
	vector<ull> res;
	auto dfs=[&](auto self,ull v) -> void {
		if(v==1)return;
		ull x=finddivisor(v);
		if(x==v)return res.push_back(x);
		self(self,x);
		self(self,v/x);
	};
	dfs(dfs,n);
	sort(all(res));
	return res;
}

} // namespace maroonrk

vector<pli> factrize_noya2(ll n){
    auto ps = maroonrk::factorize(ull(n));
    vector<pli> pes;
    int sz = ps.size();
    for (int l = 0, r = 0; l < sz; l = r){
        while (r < sz && ps[l] == ps[r]) r++;
        pes.emplace_back(ps[l],r-l);
    }
    return pes;
}

#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"

namespace noya2 {

constexpr ll safe_mod(ll x, ll m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

constexpr ll pow_mod_constexpr(ll x, ll n, int m) {
    if (m == 1) return 0;
    uint _m = (uint)(m);
    ull r = 1;
    ull y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    ll d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr ll bases[3] = {2, 7, 61};
    for (ll a : bases) {
        ll t = d;
        ll y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; 
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (ll)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);

} // namespace noya2
#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

namespace noya2{

struct barrett {
    uint _m;
    ull  im;
    explicit barrett(uint m) : _m(m), im((ull)(-1) / m + 1) {}
    uint umod() const { return _m; }
    uint mul(uint a, uint b) const {
        ull z = a;
        z *= b;
        ull x = ull((__uint128_t(z) * im) >> 64);
        uint v = (uint)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

template <int m>
struct static_modint {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    constexpr static_modint() : _v(0) {}
    template<signed_integral T>
    constexpr static_modint(T v){
        ll x = (ll)(v % (ll)(umod()));
        if (x < 0) x += umod();
        _v = (uint)(x);
    }
    template<unsigned_integral T>
    constexpr static_modint(T v){
        _v = (uint)(v % umod());
    }
    constexpr unsigned int val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    constexpr mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint& operator*=(const mint& rhs) {
        ull z = _v;
        z *= rhs._v;
        _v = (uint)(z % umod());
        return *this;
    }
    constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    constexpr mint pow(ll n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = is_prime_flag<m>;
};


template <int id> struct dynamic_modint {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template<signed_integral T>
    dynamic_modint(T v){
        ll x = (ll)(v % (ll)(mod()));
        if (x < 0) x += mod();
        _v = (uint)(x);
    }
    template<unsigned_integral T>
    dynamic_modint(T v){
        _v = (uint)(v % mod());
    }
    uint val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = noya2::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

template<typename T>
concept Modint = requires (T &a){
    T::mod();
    a.inv();
    a.val();
    a.pow(declval<int>());
};

} // namespace noya2
#line 153 "c.cpp"
using mint = modint998244353;

ll m;
vector<pli> m_pes;

vector<int> get_es(ll n){
    // m % n == 0
    vector<int> es(m_pes.size());
    for (int i = 0; auto [p, e] : m_pes){
        int c = 0;
        while (n % p == 0){
            c++;
            n /= p;
        }
        es[i] = c;
        i++;
    }
    return es;
}

void solve(){
    int n, b, c, d; in(n,b,c,d);
    vector<ll> a(n); in(a);
    vector<mint> w(n);
    w[0] = b;
    rep(i,n-1) w[i+1] = w[i] * c + d;
    int sz = m_pes.size();
    vector<mint> dp(1<<sz,1);
    rep(i,n){
        if (m % a[i] != 0) continue;
        auto es = get_es(a[i]);
        int s = 0;
        rep(j,sz){
            if (es[j] == m_pes[j].second){
                s |= (1<<j);
            }
        }
        dp[s] *= 1 + w[i];
    }
    rep(i,sz) rep(s,1<<sz) if (s >> i & 1) dp[s] *= dp[s^(1<<i)];
    mint ans = 0;
    uint msk = (1<<sz)-1;
    rep(s,1<<sz){
        ans += (dp[s] - 1) * (popcount(uint(s^msk)) % 2 == 0 ? 1 : -1);
    }
    out(ans);
}

int main(){
    int t = 1; in(t);
    in(m); m_pes = factrize_noya2(m);
    while (t--) { solve(); }
}