結果

問題 No.2578 Jewelry Store
ユーザー KudeKude
提出日時 2023-12-06 02:16:07
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 993 ms / 3,500 ms
コード長 6,130 bytes
コンパイル時間 4,549 ms
コンパイル使用メモリ 285,536 KB
実行使用メモリ 6,676 KB
最終ジャッジ日時 2023-12-06 02:16:23
合計ジャッジ時間 15,367 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge14
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テストケース

テストケース表示
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 10 ms
6,676 KB
testcase_04 AC 22 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 8 ms
6,676 KB
testcase_09 AC 20 ms
6,676 KB
testcase_10 AC 39 ms
6,676 KB
testcase_11 AC 8 ms
6,676 KB
testcase_12 AC 6 ms
6,676 KB
testcase_13 AC 7 ms
6,676 KB
testcase_14 AC 7 ms
6,676 KB
testcase_15 AC 6 ms
6,676 KB
testcase_16 AC 37 ms
6,676 KB
testcase_17 AC 21 ms
6,676 KB
testcase_18 AC 6 ms
6,676 KB
testcase_19 AC 13 ms
6,676 KB
testcase_20 AC 19 ms
6,676 KB
testcase_21 AC 21 ms
6,676 KB
testcase_22 AC 9 ms
6,676 KB
testcase_23 AC 14 ms
6,676 KB
testcase_24 AC 9 ms
6,676 KB
testcase_25 AC 10 ms
6,676 KB
testcase_26 AC 9 ms
6,676 KB
testcase_27 AC 233 ms
6,676 KB
testcase_28 AC 298 ms
6,676 KB
testcase_29 AC 279 ms
6,676 KB
testcase_30 AC 328 ms
6,676 KB
testcase_31 AC 226 ms
6,676 KB
testcase_32 AC 142 ms
6,676 KB
testcase_33 AC 187 ms
6,676 KB
testcase_34 AC 228 ms
6,676 KB
testcase_35 AC 58 ms
6,676 KB
testcase_36 AC 195 ms
6,676 KB
testcase_37 AC 91 ms
6,676 KB
testcase_38 AC 118 ms
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testcase_39 AC 106 ms
6,676 KB
testcase_40 AC 117 ms
6,676 KB
testcase_41 AC 101 ms
6,676 KB
testcase_42 AC 90 ms
6,676 KB
testcase_43 AC 158 ms
6,676 KB
testcase_44 AC 76 ms
6,676 KB
testcase_45 AC 132 ms
6,676 KB
testcase_46 AC 100 ms
6,676 KB
testcase_47 AC 580 ms
6,676 KB
testcase_48 AC 294 ms
6,676 KB
testcase_49 AC 993 ms
6,676 KB
testcase_50 AC 856 ms
6,676 KB
testcase_51 AC 103 ms
6,676 KB
testcase_52 AC 374 ms
6,676 KB
testcase_53 AC 36 ms
6,676 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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';
  }
}
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