#1113056 (C++23) No.3236 累乗数大好きbot

• 問題: No.3236 累乗数大好きbot
• ユーザー: zoidzium (zz)
• 提出日時: 2025-08-15 22:59:57
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 25,172 bytes
• コンパイル時間: 3,281 ms
• コンパイル使用メモリ: 301,328 KB
• 実行使用メモリ: 12,120 KB
• 最終ジャッジ日時: 2025-08-15 23:00:27
• 合計ジャッジ時間: 11,157 ms
• ジャッジサーバーID （参考情報）: judge6 / judge5

ファイルパターン	結果
sample	AC * 1
other	AC * 4 TLE * 1 -- * 26

ソースコード

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;

using xy = pair<ll, ll>;
using vxy = vector<xy>;
using vvxy = vector<vxy>;

using bs8 = bitset<8>;
using bs16 = bitset<16>;
using bs32 = bitset<32>;
using bs64 = bitset<64>;
using vbs8 = vector<bs8>;
using vbs16 = vector<bs16>;
using vbs32 = vector<bs32>;
using vbs64 = vector<bs64>;

using vs = vector<string>;
using vvs = vector<vs>;

using ull = unsigned long long;
using vul = vector<ull>;

using vd = vector<double>;
using vvd = vector<vd>;

using coord = pair<double, double>;
using vcoord = vector<coord>;

#define rep(var, n) for (ll var = 0; var < (ll)(n); var++)
#define cnt(var, n, m) for (ll var = (n); var <= (ll)(m); var++)
#define rcnt(var, n, m) for (ll var = (n); var >= (ll)(m); var--)
#define each(ite, C) for (auto ite = (C).begin(); ite != (C).end(); ite++)
#define reach(ite, C) for (auto ite = (C).rbegin(); ite != (C).rend(); ite++)
#define yn(b) cout << (((b) > 0) ? "Yes" : "No") << endl;

/////////////////////////////////////////////////
namespace zz_print {
class dbg {
 public:
  static bool unprint;
  static string margin;
  static string separated;
  static string indentS;
  static int hierarchical;
  static int topHier;
  static int precision;
  static bool exponential;

  static void setFloat(const int& prec, const bool& expo) {
    precision = prec;
    exponential = expo;
  };

 private:
  static void ZOUT(const ll& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const ull& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const int& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const unsigned int& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const double& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const float& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const char& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const string& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const bs8& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const bs16& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const bs32& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  static void ZOUT(const bs64& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };
  template <typename T>
  static void ZOUT(const T& x, const bool& tail = false) {
    cout << x;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
  };

  static bool BRANKET_BEGIN(const char& c_L) {
    cout << c_L << margin;
    if (hierarchical > 0) {
      hierarchical--;
      indentS.push_back(' ');
      indentS += margin;
      cout << endl << indentS;
      return false;
    }
    return true;
  };
  static void BRANKET_END(const char& c_R, const bool& flat,
                          const bool& tail = false) {
    if (!flat) {
      rep(i, 1 + margin.size()) indentS.pop_back();
      cout << endl << indentS;
    }
    cout << c_R;
    if (tail) {
      cout << margin << flush;
    } else {
      cout << separated << flush;
    }
    if (!flat) {
      hierarchical++;
      if (hierarchical == topHier) cout << endl << indentS;
    }
  };

  template <typename Elm>
  static void ZOUT(const vector<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('[');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END(']', flat, tail);
  };
  template <typename Elm>
  static void ZOUT(const list<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('(');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END(')', flat, tail);
  };

  template <typename LftElm, typename RgtElm>
  static void ZOUT(const pair<LftElm, RgtElm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('<');

    ZOUT(x.first);
    if (!flat) cout << endl << indentS;
    ZOUT(x.second, true);

    BRANKET_END('>', flat, tail);
  };

  template <typename LftElm, typename RgtElm>
  static void ZOUT(const map<LftElm, RgtElm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };
  template <typename LftElm, typename RgtElm>
  static void ZOUT(const multimap<LftElm, RgtElm>& x,
                   const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };
  template <typename LftElm, typename RgtElm>
  static void ZOUT(const unordered_map<LftElm, RgtElm>& x,
                   const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };
  template <typename LftElm, typename RgtElm>
  static void ZOUT(const unordered_multimap<LftElm, RgtElm>& x,
                   const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };

  template <typename Elm>
  static void ZOUT(const set<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };
  template <typename Elm>
  static void ZOUT(const multiset<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };
  template <typename Elm>
  static void ZOUT(const unordered_set<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };
  template <typename Elm>
  static void ZOUT(const unordered_multiset<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('{');

    ll I = 0;
    ll N = x.size() - 1;
    each(ite, x) {
      ZOUT(*ite, (I == N));
      if (!flat && I != N) cout << endl << indentS;
      I++;
    }

    BRANKET_END('}', flat, tail);
  };

  template <typename Elm>
  static void ZOUT(const stack<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('[');

    stack<Elm> y = x;
    while (!y.empty()) {
      ZOUT(y.top(), y.size() == 1);
      y.pop();
      if (!flat && !y.empty()) cout << endl << indentS;
    }

    BRANKET_END(')', flat, tail);
  };
  template <typename Elm>
  static void ZOUT(const queue<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('[');

    queue<Elm> y = x;
    while (!y.empty()) {
      ZOUT(y.front(), y.size() == 1);
      y.pop();
      if (!flat && !y.empty()) cout << endl << indentS;
    }

    BRANKET_END(')', flat, tail);
  };
  template <typename Elm>
  static void ZOUT(const priority_queue<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('[');

    priority_queue<Elm> y = x;
    while (!y.empty()) {
      ZOUT(y.top(), y.size() == 1);
      y.pop();
      if (!flat && !y.empty()) cout << endl << indentS;
    }

    BRANKET_END(')', flat, tail);
  };
  template <typename Elm>
  static void ZOUT(const deque<Elm>& x, const bool& tail = false) {
    bool flat = BRANKET_BEGIN('[');

    deque<Elm> y = x;
    while (!y.empty()) {
      ZOUT(y.front(), y.size() == 1);
      y.pop_front();
      if (!flat && !y.empty()) cout << endl << indentS;
    }

    BRANKET_END(']', flat, tail);
  };

  static void ZOUT_BRANCH() {}
  template <typename HeadArg, typename... Args>
  static void ZOUT_BRANCH(HeadArg&& head, Args&&... args) {
    ZOUT(head);
    ZOUT_BRANCH(forward<Args>(args)...);
  };

 public:
  template <int hier = 0, int sep = 2, int mgn = 1, typename... Args>
  static void zout(Args&&... args) {
    if (unprint) return;
    margin = string(mgn, ' ');
    separated = string(sep, ' ');
    hierarchical = hier;
    topHier = hier;
    indentS = "";
    cout << setprecision(precision);
    if (exponential) {
      cout << scientific;
    } else {
      cout << fixed;
    }

    ZOUT_BRANCH(forward<Args>(args)...);

    cout << endl << defaultfloat;
  };
};

bool dbg::unprint = false;
string dbg::margin = "";
string dbg::separated = "";
string dbg::indentS = "";
int dbg::hierarchical = 0;
int dbg::topHier = 0;
int dbg::precision = 6;
bool dbg::exponential = false;

};  // namespace zz_print
using namespace zz_print;

namespace zz_time {
/// @brief プログラム実行時のタイムポイント
std::chrono::_V2::system_clock::time_point START_TIME =
    std::chrono::system_clock::now();
/// @brief プログラム実行から経過時間をミリ秒で取得
/// @param st 経過開始時刻(基本引数指定する必要なし)
/// @return 経過時間ミリ秒
ll currentTime(std::chrono::_V2::system_clock::time_point st = START_TIME) {
  std::chrono::_V2::system_clock::time_point now =
      std::chrono::system_clock::now();
  return (ll)(std::chrono::duration_cast<std::chrono::milliseconds>(now - st)
                  .count());
};
/// @brief 実行時間が超過していないかの判定
/// @param mSec 実行時間制約ミリ秒
/// @return 実行時間制約以下であればtrue,その他はfalse
bool punctualityTime(const ll& mSec) { return (currentTime() < mSec); }

/// @brief 実行時間が超過しているかの判定
/// @param mSec 実行時間制約ミリ秒
/// @return 実行時間制約超過していればtrue,その他はfalse
bool spendTime(const ll& mSec) { return (currentTime() >= mSec); }
};  // namespace zz_time
using namespace zz_time;

namespace zz_random {
random_device seed_gen;
default_random_engine RANDOM_ENGINE(seed_gen());

/// @brief 整数閉区間[L,R]一様ランダム器生成
/// @param L 下限値 (default 0)
/// @param R 上限値 (default 1)
/// @return ランダム生成器, RAMDOM_ENGINEを引数としてランダム生成
uniform_int_distribution<> createIntCloseSegRandom(const ll& L = 0,
                                                   const ll& R = 1) {
  return uniform_int_distribution<>(L, R);
};

/// @brief 実数閉区間[L,R]一様ランダム器生成
/// @param L 下限値 (default 0.0)
/// @param R 上限値 (default 1.0)
/// @return ランダム生成器, RAMDOM_ENGINEを引数としてランダム生成
uniform_real_distribution<> createRealCloseSegRandom(const double& L = 0.0,
                                                     const double& R = 1.0) {
  return uniform_real_distribution<>(L, R);
};

/// @brief 正規表現ランダム器生成
/// @param average 平均値
/// @param s 標準偏差
/// @return ランダム生成器, RAMDOM_ENGINEを引数としてランダム生成
normal_distribution<> createNormalRandom(const double& average = 0.0,
                                         const double& s = 1.0) {
  return normal_distribution<>(average, s);
};

};  // namespace zz_random
using namespace zz_random;

namespace zz_mod {
class pp {
 public:
  ll val;
  ll mod;
  static bool ignorePPModPrint;

  void recalc() {
    val %= mod;
    if (val < 0) val += mod;
  };

  /// @brief modint (+-*/ != exp ~ inv recalc )
  /// @param x value
  /// @param y mod (default= 998244353)
  pp(const ll& x = 0, const ll& y = 998244353) {
    val = x;
    mod = y;
    recalc();
  };

  friend pp operator+(const pp& x, const pp& y) {
    return pp(x.val + y.val, x.mod);
  };
  friend pp operator+(const pp&& x, const pp& y) {
    return pp(x.val + y.val, x.mod);
  };
  friend pp operator+(const pp& x, const pp&& y) {
    return pp(x.val + y.val, x.mod);
  };
  friend pp operator+(const pp&& x, const pp&& y) {
    return pp(x.val + y.val, x.mod);
  };

  template <typename T>
  friend pp operator+(const pp& x, const T& y) {
    return pp(x.val + y, x.mod);
  };
  template <typename T>
  friend pp operator+(const pp&& x, const T& y) {
    return pp(x.val + y, x.mod);
  };
  template <typename T>
  friend pp operator+(const pp& x, const T&& y) {
    return pp(x.val + y, x.mod);
  };
  template <typename T>
  friend pp operator+(const pp&& x, const T&& y) {
    return pp(x.val + y, x.mod);
  };

  friend pp operator-(const pp& x) { return pp(-x.val, x.mod); };
  friend pp operator-(const pp&& x) { return pp(-x.val, x.mod); };

  friend pp operator-(const pp& x, const pp& y) {
    return pp(x.val - y.val, x.mod);
  };
  friend pp operator-(const pp&& x, const pp& y) {
    return pp(x.val - y.val, x.mod);
  };
  friend pp operator-(const pp& x, const pp&& y) {
    return pp(x.val - y.val, x.mod);
  };
  friend pp operator-(const pp&& x, const pp&& y) {
    return pp(x.val - y.val, x.mod);
  };

  template <typename T>
  friend pp operator-(const pp& x, const T& y) {
    return pp(x.val - y, x.mod);
  };
  template <typename T>
  friend pp operator-(const pp&& x, const T& y) {
    return pp(x.val - y, x.mod);
  };
  template <typename T>
  friend pp operator-(const pp& x, const T&& y) {
    return pp(x.val - y, x.mod);
  };
  template <typename T>
  friend pp operator-(const pp&& x, const T&& y) {
    return pp(x.val - y, x.mod);
  };

  friend pp operator*(const pp& x, const pp& y) {
    return pp(x.val * y.val, x.mod);
  };
  friend pp operator*(const pp&& x, const pp& y) {
    return pp(x.val * y.val, x.mod);
  };
  friend pp operator*(const pp& x, const pp&& y) {
    return pp(x.val * y.val, x.mod);
  };
  friend pp operator*(const pp&& x, const pp&& y) {
    return pp(x.val * y.val, x.mod);
  };

  template <typename T>
  friend pp operator*(const pp& x, const T& y) {
    return pp(x.val * y, x.mod);
  };
  template <typename T>
  friend pp operator*(const pp&& x, const T& y) {
    return pp(x.val * y, x.mod);
  };
  template <typename T>
  friend pp operator*(const pp& x, const T&& y) {
    return pp(x.val * y, x.mod);
  };
  template <typename T>
  friend pp operator*(const pp&& x, const T&& y) {
    return pp(x.val * y, x.mod);
  };

  friend pp operator~(const pp& x) { return x.exp(-1); }
  friend pp operator~(const pp&& x) { return x.exp(-1); }

  friend pp operator/(const pp& x, const pp& y) { return x * (~y); };
  friend pp operator/(const pp&& x, const pp& y) { return x * (~y); };
  friend pp operator/(const pp& x, const pp&& y) { return x * (~y); };
  friend pp operator/(const pp&& x, const pp&& y) { return x * (~y); };

  template <typename T>
  friend pp operator/(const pp& x, const T& y) {
    return x * pp(y, x.mod).inv();
  };
  template <typename T>
  friend pp operator/(const pp&& x, const T& y) {
    return x * pp(y, x.mod).inv();
  };
  template <typename T>
  friend pp operator/(const pp& x, const T&& y) {
    return x * pp(y, x.mod).inv();
  };
  template <typename T>
  friend pp operator/(const pp&& x, const T&& y) {
    return x * pp(y, x.mod).inv();
  };

  friend pp& operator+=(pp& x, const pp& y) {
    x.val += y.val;
    x.recalc();
    return x;
  };
  friend pp& operator+=(pp& x, const pp&& y) {
    x.val += y.val;
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator+=(pp& x, const T& y) {
    x.val += y;
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator+=(pp& x, const T&& y) {
    x.val += y;
    x.recalc();
    return x;
  };

  friend pp& operator-=(pp& x, const pp& y) {
    x.val -= y.val;
    x.recalc();
    return x;
  };
  friend pp& operator-=(pp& x, const pp&& y) {
    x.val -= y.val;
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator-=(pp& x, const T& y) {
    x.val -= y;
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator-=(pp& x, const T&& y) {
    x.val -= y;
    x.recalc();
    return x;
  };

  friend pp& operator*=(pp& x, const pp& y) {
    x.val *= y.val;
    x.recalc();
    return x;
  };
  friend pp& operator*=(pp& x, const pp&& y) {
    x.val *= y.val;
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator*=(pp& x, const T& y) {
    x.val *= y;
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator*=(pp& x, const T&& y) {
    x.val *= y;
    x.recalc();
    return x;
  };

  friend pp& operator/=(pp& x, const pp& y) {
    x *= pp(y.val, x.mod).inv();
    x.recalc();
    return x;
  };
  friend pp& operator/=(pp& x, const pp&& y) {
    x *= pp(y.val, x.mod).inv();
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator/=(pp& x, const T& y) {
    x *= pp(y, x.mod).inv();
    x.recalc();
    return x;
  };
  template <typename T>
  friend pp& operator/=(pp& x, const T&& y) {
    x *= pp(y, x.mod).inv();
    x.recalc();
    return x;
  };

  pp exp(ll x) const {
    if (x == 0) {
      return pp(1, this->mod);
    }
    pp y = *this;

    if (x > 0) {
      vl Vec;
      while (x > 0) {
        Vec.push_back(x & 1);
        x >>= 1;
      }
      pp ans(1, this->mod);
      each(ite, Vec) {
        if (*ite) ans = ans * y;
        y = y * y;
      }

      return ans;
    }

    return y.exp(y.mod - 2).exp(-x);
  };

  pp inv() const {
    return ~(*this);
    return pp(this->val, this->mod).exp(-1);
  }

  friend ostream& operator<<(ostream& os, const pp& x) {
    if (ignorePPModPrint) {
      os << "{" << x.val << "}";
    } else {
      os << "{" << x.val << " %" << x.mod << "}";
    }
    return os;
  };
};
bool pp::ignorePPModPrint = false;

class factorial {
 public:
  const ll size;
  vector<pp> vec;
  /// @brief mod! (operator[] comb)
  /// @param x max! [0,x]  (default 1000000)
  /// @param y mod (default 998244353)
  factorial(const ll&& x = 1000000, const ll&& y = 998244353) : size(x + 1) {
    vec = vector<pp>(x + 1, pp(1, y));
    cnt(i, 2, x) vec[i] *= (vec[i - 1] * pp(i, y));
  };

  /// @brief mod factorial
  /// @return x! mod
  pp operator[](const ll& x) const { return vec[x]; };

  /// @brief mod factorial
  /// @return x! mod
  pp operator[](const ll&& x) const { return vec[x]; };

  /// @brief mod combination
  /// @param n
  /// @param m
  /// @return nCm
  pp comb(const ll n, const ll m) const {
    return (vec[n] / (vec[m] * vec[n - m]));
  };
};

class convolution998244353 {
  int div_lmt;
  pp zeta;
  vector<pp> roots;
  vector<pp> inv_roots;

  vector<pp> ntt(const vector<pp>& vec, const bool& inverse,
                 const int& sizelog2, int div_cnt = -1) {
    if (div_cnt == -1) div_cnt = div_lmt;

    vector<pp> nxt_vec;
    while (nxt_vec.size() < vec.size()) nxt_vec.push_back(pp(0, zeta.mod));
    // nxt_vec.resize(vec.size());
    pp zt(1, zeta.mod);
    if (vec.size() == 1 || div_cnt == 0) {
      rep(i, nxt_vec.size()) {
        pp ztij = zt;

        rep(j, vec.size()) {
          nxt_vec[i] += vec[j] * ztij;
          ztij *= zt;
        }
        zt *= (inverse ? roots[0] : inv_roots[0]);
      }
      return nxt_vec;
    }

    vector<pp> vec1(vec.size() / 2);
    vector<pp> vec2(vec.size() / 2);
    rep(i, vec.size() / 2) {
      vec1[i] = vec[2 * i];
      vec2[i] = vec[2 * i + 1];
    }
    vector<pp> dft1 = ntt(vec1, inverse, sizelog2 - 1, div_cnt - 1);
    vector<pp> dft2 = ntt(vec2, inverse, sizelog2 - 1, div_cnt - 1);
    rep(i, vec.size()) {
      nxt_vec[i] = dft1[i % dft1.size()] + zt * dft2[i % dft2.size()];
      zt *= (inverse ? roots[sizelog2] : inv_roots[sizelog2]);
    }
    return nxt_vec;
  };

 public:
  convolution998244353()
      : div_lmt(23),
        zeta(pp(3, 998244353)),
        roots(vector<pp>(div_lmt + 1, pp(0, 998244353))),
        inv_roots(vector<pp>(div_lmt + 1, pp(0, 998244353))) {
    roots[div_lmt] = zeta.exp((zeta.mod - 1) / (1LL << 23));

    inv_roots[div_lmt] = roots[div_lmt].inv();
    rcnt(i, div_lmt - 1, 0) {
      roots[i] = roots[i + 1] * roots[i + 1];
      inv_roots[i] = inv_roots[i + 1] * inv_roots[i + 1];
    }
  };

  vector<pp> conv(vector<pp> vec1, vector<pp> vec2) {
    int size = 1, sizelog2 = 0;

    while ((int)(vec1.size() + vec2.size()) > size) {
      size <<= 1;
      sizelog2++;
    }

    while ((int)vec1.size() < size) vec1.push_back(pp(0, zeta.mod));
    while ((int)vec2.size() < size) vec2.push_back(pp(0, zeta.mod));
    // vec1.resize(size);
    // vec2.resize(size);
    vector<pp> dft1 = ntt(vec1, 1, sizelog2);
    vector<pp> dft2 = ntt(vec2, 1, sizelog2);

    vector<pp> dft(size);
    rep(i, size) dft[i] = dft1[i] * dft2[i];
    vector<pp> conv_vec = ntt(dft, 0, sizelog2);
    rep(i, conv_vec.size()) conv_vec[i] /= size;
    return conv_vec;
  }
};
};  // namespace zz_mod
using namespace zz_mod;

namespace zz_prime {
class prime {
 public:
  static vl sieve;
  static vl p;
  static void set(ll N = 1000000) {
    N = max<ll>(2, N) + 1;
    sieve = vl(N, 0);
    p.clear();
    sieve[0] = 1;
    sieve[1] = 1;
    cnt(i, 2, N - 1) {
      if (sieve[i] == 0) {
        p.push_back(i);
        ll j = i;
        while (j < N) {
          if (sieve[j] == 0) sieve[j] = i;
          j += i;
        }
      }
    }
  };

  static bool isprime(ll x) {
    if (x <= 1) return false;
    if (sieve.empty()) set();
    if (x < sieve.size()) return (sieve[x] == x);
    each(ite, p) {
      if (x < (*ite) * (*ite)) return true;
      if ((x % (*ite)) == 0) return false;
    }
    return true;
  };

  static vxy factor(ll x) {
    x = max<ll>(1, x);
    if (sieve.empty()) set();

    map<ll, ll> MAP;
    each(ite, p) {
      if (x < sieve.size()) break;

      while ((x % (*ite)) == 0) {
        MAP[*ite]++;
        x /= *ite;
      }
    }

    if (x < sieve.size()) {
      while (x > 1) {
        MAP[sieve[x]]++;
        x /= sieve[x];
      }
    } else {
      MAP[x]++;
    }
    vxy fact;
    each(ite, MAP) fact.push_back(*ite);
    return fact;
  };

  static vl divisors(const vxy& fact) {
    vl ans(1, 1);
    function<void(const ll&, const ll&)> Func =
        [&fact, &ans, &Func](const ll& I, const ll& Elm) -> void {
      if (fact.empty()) return;
      ll Add = 1;

      if ((I + 1) < fact.size()) {
        Func(I + 1, Elm);
      } else {
        if (Elm != 1) ans.emplace_back(Elm);
      }

      cnt(i, 1, fact[I].second) {
        Add *= fact[I].first;
        if ((I + 1) < fact.size()) {
          Func(I + 1, Elm * Add);
        } else {
          ans.emplace_back(Elm * Add);
        }
      };
    };
    Func(0, 1);
    sort(ans.begin(), ans.end());
    return ans;
  };
};

vl prime::p;
vl prime::sieve;
}  // namespace zz_prime
using namespace zz_prime;

unordered_map<ll, ll> MAP;
/////////////////////////////////////////////////
void solve(const ll& N) {
  auto ITE = MAP.find(N);
  if (ITE != MAP.end()) {
    cout << ITE->second << endl;
    return;
  }
  vxy Vec = prime::factor(N);
  // dbg::zout<1>(N, Vec);
  ll D = LONG_LONG_MAX;

  each(ite, Vec) { D = min<ll>(D, ite->second); }
  each(ite, Vec) { D = __gcd(D, ite->second); }
  MAP[N] = D;
  cout << D << endl;
};
/////////////////////////////////////////////////

int main() {
  dbg::unprint = true;

  prime::set(1000000);
  ll Q;
  cin >> Q;
  vl N(Q);
  rep(i, Q) cin >> N[i];
  rep(i, Q) solve(N[i]);
  return 0;
}