#1168377 (C++23) No.3565 Take from Excluded

• 問題: No.3565 Take from Excluded
• ユーザー: yamate11
• 提出日時: 2026-06-05 23:22:47
• 言語: C++23 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 243 ms / 2,000 ms
• コード長: 27,153 bytes
• コンパイル時間: 2,956 ms
• コンパイル使用メモリ: 362,344 KB
• 実行使用メモリ: 6,400 KB
• 最終ジャッジ日時: 2026-06-05 23:23:15
• 合計ジャッジ時間: 7,693 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge1_1

ファイルパターン	結果
sample	AC * 2
other	AC * 14 TLE * 1 -- * 3

ソースコード

#include <bits/stdc++.h>
#include <cassert>
using namespace std;
using ll = long long int;
using u64 = unsigned long long;
using pll = pair<ll, ll>;
// #include <atcoder/all>
// using namespace atcoder;
#define REP(i, a, b) for (ll i = (a); i < (b); i++)
#define REPrev(i, a, b) for (ll i = (a); i >= (b); i--)
#define ALL(coll) (coll).begin(), (coll).end()
#define SIZE(v) ((ll)((v).size()))
#define REPOUT(i, a, b, exp, sep) REP(i, (a), (b)) cout << (exp) << (i + 1 == (b) ? "" : (sep)); cout << "\n"

// @@ !! LIM(mod debug cmpNaive)

// ---- inserted library file algOp.cc
// published at https://github.com/yamate11/compprog-clib/blob/master/algOp.cc

// Common definitions
//    zero, one, inverse

template<typename T>
const T zero(const T& t) {
  if constexpr (is_integral_v<T> || is_floating_point_v<T>) { return (T)0; }
  else { return t.zero(); }
}

template<typename T>
const T one(const T& t) {
  if constexpr (is_integral_v<T> || is_floating_point_v<T>) { return (T)1; }
  else { return t.one(); }
}

template<typename T>
const T inverse(const T& t) {
  if constexpr (is_floating_point_v<T>) { return 1.0 / t; }
  else { return t.inverse(); }
}

#ifdef BOOST_MP_CPP_INT_HPP
template<> const cpp_int zero(const cpp_int&) { return cpp_int(0); }
template<> const cpp_int one(const cpp_int&) { return cpp_int(1); }
#endif // BOOST_MP_CPP_INT_HPP

// begin -- detection ideom
//    cf. https://blog.tartanllama.xyz/detection-idiom/

namespace tartan_detail {
  template <template <class...> class Trait, class Enabler, class... Args>
  struct is_detected : false_type{};

  template <template <class...> class Trait, class... Args>
  struct is_detected<Trait, void_t<Trait<Args...>>, Args...> : true_type{};
}

template <template <class...> class Trait, class... Args>
using is_detected = typename tartan_detail::is_detected<Trait, void, Args...>::type;

// end -- detection ideom


template<typename T>
// using subst_add_t = decltype(T::subst_add(declval<typename T::value_type &>(), declval<typename T::value_type>()));
using subst_add_t = decltype(T::subst_add);
template<typename T>
using has_subst_add = is_detected<subst_add_t, T>;

template<typename T>
using add_t = decltype(T::add);
template<typename T>
using has_add = is_detected<add_t, T>;

template<typename T>
using subst_mult_t = decltype(T::subst_mult);
template<typename T>
using has_subst_mult = is_detected<subst_mult_t, T>;

template<typename T>
using mult_t = decltype(T::mult);
template<typename T>
using has_mult = is_detected<mult_t, T>;

template<typename T>
using subst_subt_t = decltype(T::subst_subt);
template<typename T>
using has_subst_subt = is_detected<subst_subt_t, T>;

template<typename T>
using subt_t = decltype(T::subt);
template<typename T>
using has_subt = is_detected<subt_t, T>;

template <typename Opdef>
struct MyAlg {
  using T = typename Opdef::value_type;
  using value_type = T;
  T v;
  MyAlg() {}
  MyAlg(const T& v_) : v(v_) {}
  MyAlg(T&& v_) : v(move(v_)) {}
  bool operator==(MyAlg o) const { return v == o.v; }
  bool operator!=(MyAlg o) const { return v != o.v; }
  operator T() const { return v; }
  MyAlg zero() const { return MyAlg(Opdef::zero(v)); }
  MyAlg one() const { return MyAlg(Opdef::one(v)); }
  MyAlg inverse() const { return MyAlg(Opdef::inverse(v)); }
  MyAlg operator/=(const MyAlg& o) { return *this *= o.inverse(); }
  MyAlg operator/(const MyAlg& o) const { return (*this) * o.inverse(); }
  MyAlg operator-() const { return zero() - *this; }

  MyAlg& operator +=(const MyAlg& o) { 
    if constexpr (has_subst_add<Opdef>::value) {
      Opdef::subst_add(v, o.v);
      return *this;
    }else if constexpr (has_add<Opdef>::value) {
      v = Opdef::add(v, o.v);
      return *this;
    }else static_assert("either subst_add or add is needed.");

  }
  MyAlg operator +(const MyAlg& o) const { 
    if constexpr (has_add<Opdef>::value) {
      return MyAlg(Opdef::add(v, o.v));
    }else if constexpr (has_subst_add<Opdef>::value) {
      MyAlg ret(v);
      Opdef::subst_add(ret.v, o.v);
      return ret;
    }else static_assert("either subst_add or add is needed.");
  }
  MyAlg& operator *=(const MyAlg& o) { 
    if constexpr (has_subst_mult<Opdef>::value) {
      Opdef::subst_mult(v, o.v);
      return *this;
    }else if constexpr (has_mult<Opdef>::value) {
      v = Opdef::mult(v, o.v);
      return *this;
    }else static_assert("either subst_mult or mult is needed.");

  }
  MyAlg operator *(const MyAlg& o) const { 
    if constexpr (has_mult<Opdef>::value) {
      return MyAlg(Opdef::mult(v, o.v));
    }else if constexpr (has_subst_mult<Opdef>::value) {
      MyAlg ret(v);
      Opdef::subst_mult(ret.v, o.v);
      return ret;
    }else static_assert("either subst_mult or mult is needed.");
  }
  MyAlg& operator -=(const MyAlg& o) { 
    if constexpr (has_subst_subt<Opdef>::value) {
      Opdef::subst_subt(v, o.v);
      return *this;
    }else if constexpr (has_subt<Opdef>::value) {
      v = Opdef::subt(v, o.v);
      return *this;
    }else static_assert("either subst_subt or subt is needed.");

  }
  MyAlg operator -(const MyAlg& o) const { 
    if constexpr (has_subt<Opdef>::value) {
      return MyAlg(Opdef::subt(v, o.v));
    }else if constexpr (has_subst_subt<Opdef>::value) {
      MyAlg ret(v);
      Opdef::subst_subt(ret.v, o.v);
      return ret;
    }else static_assert("either subst_subt or subt is needed.");
  }
  friend istream& operator >>(istream& is, MyAlg& t)       { is >> t.v; return is; }
  friend ostream& operator <<(ostream& os, const MyAlg& t) { os << t.v; return os; }
};





// ---- end algOp.cc

// ---- inserted function f:gcd from util.cc

// auto [g, s, t] = eGCD(a, b)
//     g == gcd(|a|, |b|) and as + bt == g           
//     It guarantees that max(|s|, |t|) <= max(|a| / g, |b| / g)   (when g != 0)
//     Note that gcd(a, 0) == gcd(0, a) == a.
template<typename INT=ll>
tuple<INT, INT, INT> eGCD(INT a, INT b) {
  INT sa = a < 0 ? -1 : 1;
  INT ta = 0;
  INT za = a * sa;
  INT sb = 0;
  INT tb = b < 0 ? -1 : 1;
  INT zb = b * tb;
  while (zb != 0) {
    INT q = za / zb;
    INT r = za % zb;
    za = zb;
    zb = r;
    INT new_sb = sa - q * sb;
    sa = sb;
    sb = new_sb;
    INT new_tb = ta - q * tb;
    ta = tb;
    tb = new_tb;
  }
  return {za, sa, ta};
}

pair<ll, ll> crt_sub(ll a1, ll x1, ll a2, ll x2) {
  // DLOGKL("crt_sub", a1, x1, a2, x2);
  a1 = a1 % x1;
  a2 = a2 % x2;
  auto [g, s, t] = eGCD(x1, -x2);
  ll gq = (a2 - a1) / g;
  ll gr = (a2 - a1) % g;
  if (gr != 0) return {-1, -1};
  s *= gq;
  t *= gq;
  ll z = x1 / g * x2;
  // DLOGK(z);
  s = s % (x2 / g);
  ll r = (x1 * s + a1) % z;
  // DLOGK(r);
  if (r < 0) r += z;
  // DLOGK(r);
  return {r, z};
};

// Chinese Remainder Theorem
//
//    r = crt(a1, x1, a2, x2)
//    ==>   r = a1 (mod x1);  r = a2 (mod x2);  0 <= r < lcm(x1, x2)
//    If no such r exists, returns -1
//    Note: x1 and x2 should >= 1.  a1 and a2 can be negative or zero.
//
//    r = crt(as, xs)
//    ==>   for all i. r = as[i] (mod xs[i]); 0 <= r < lcm(xs)
//    If no such r exists, returns -1
//    Note: xs[i] should >= 1.  as[i] can be negative or zero.
//          It should hold: len(xs) == len(as) > 0

ll crt(ll a1, ll x1, ll a2, ll x2) { return crt_sub(a1, x1, a2, x2).first; }

ll crt(vector<ll> as, vector<ll> xs) {
  // DLOGKL("crt", as, xs);
  assert(xs.size() == as.size() && xs.size() > 0);
  ll r = as[0];
  ll z = xs[0];
  for (size_t i = 1; i < xs.size(); i++) {
    // DLOGK(i, r, z, as[i], xs[i]);
    tie(r, z) = crt_sub(r, z, as[i], xs[i]);
    // DLOGK(r, z);
    if (r == -1) return -1;
  }
  return r;
}

// ---- end f:gcd

// ---- inserted library file mod.cc
// published at https://github.com/yamate11/compprog-clib/blob/master/mod.cc

template<int mod=0, typename INT=ll>
struct FpG {   // G for General
  static INT dyn_mod;

  static INT getMod() {
    if (mod == 0) return dyn_mod;
    else          return (INT)mod;
  }
  
  // Effective only when mod == 0.
  // _mod must be less than the half of the maximum value of INT.
  static void setMod(INT _mod) {  
    dyn_mod = _mod;
  }

  static INT _conv(INT x) {
    if (x >= getMod())  return x % getMod();
    if (x >= 0)         return x;
    if (x >= -getMod()) return x + getMod();
    INT y = x % getMod();
    if (y == 0) return 0;
    return y + getMod();
  }

  INT val;

  FpG(INT t = 0) : val(_conv(t)) {}
  FpG(const FpG& t) : val(t.val) {}
  FpG& operator =(const FpG& t) { val = t.val; return *this; }
  FpG& operator =(INT t) { val = _conv(t); return *this; }

  FpG& operator +=(const FpG& t) {
    val += t.val;
    if (val >= getMod()) val -= getMod();
    return *this;
  }

  FpG& operator -=(const FpG& t) {
    val -= t.val;
    if (val < 0) val += getMod();
    return *this;
  }

  FpG& operator *=(const FpG& t) {
    val = (val * t.val) % getMod();
    return *this;
  }

  FpG inv() const {
    if (val == 0) { throw runtime_error("FpG::inv(): called for zero."); }
    auto [g, u, v] = eGCD(val, getMod());
    if (g != 1) { throw runtime_error("FpG::inv(): not co-prime."); }
    return FpG(u);
  }

  FpG zero() const { return (FpG)0; }
  FpG one() const { return (FpG)1; }
  FpG inverse() const { return inv(); }

  FpG& operator /=(const FpG& t) {
    return (*this) *= t.inv();
  }

  FpG operator +(const FpG& t) const { return FpG(val) += t; }
  FpG operator -(const FpG& t) const { return FpG(val) -= t; }
  FpG operator *(const FpG& t) const { return FpG(val) *= t; }
  FpG operator /(const FpG& t) const { return FpG(val) /= t; }
  FpG operator -() const { return FpG(-val); }

  bool operator ==(const FpG& t) const { return val == t.val; }
  bool operator !=(const FpG& t) const { return val != t.val; }
  
  operator INT() const { return val; }

  friend FpG operator +(INT x, const FpG& y) { return FpG(x) + y; }
  friend FpG operator -(INT x, const FpG& y) { return FpG(x) - y; }
  friend FpG operator *(INT x, const FpG& y) { return FpG(x) * y; }
  friend FpG operator /(INT x, const FpG& y) { return FpG(x) / y; }
  friend bool operator ==(INT x, const FpG& y) { return FpG(x) == y; }
  friend bool operator !=(INT x, const FpG& y) { return FpG(x) != y; }
  friend FpG operator +(const FpG& x, INT y) { return x + FpG(y); }
  friend FpG operator -(const FpG& x, INT y) { return x - FpG(y); }
  friend FpG operator *(const FpG& x, INT y) { return x * FpG(y); }
  friend FpG operator /(const FpG& x, INT y) { return x / FpG(y); }
  friend bool operator ==(const FpG& x, INT y) { return x == FpG(y); }
  friend bool operator !=(const FpG& x, INT y) { return x != FpG(y); }

  /* The following are needed to avoid warnings in cases such as FpG x; x = 5 + x; rather than x = FpG(5) + x; */
  friend FpG operator +(int x, const FpG& y) { return FpG(x) + y; }
  friend FpG operator -(int x, const FpG& y) { return FpG(x) - y; }
  friend FpG operator *(int x, const FpG& y) { return FpG(x) * y; }
  friend FpG operator /(int x, const FpG& y) { return FpG(x) / y; }
  friend bool operator ==(int x, const FpG& y) { return FpG(x) == y; }
  friend bool operator !=(int x, const FpG& y) { return FpG(x) != y; }
  friend FpG operator +(const FpG& x, int y) { return x + FpG(y); }
  friend FpG operator -(const FpG& x, int y) { return x - FpG(y); }
  friend FpG operator *(const FpG& x, int y) { return x * FpG(y); }
  friend FpG operator /(const FpG& x, int y) { return x / FpG(y); }
  friend bool operator ==(const FpG& x, int y) { return x == FpG(y); }
  friend bool operator !=(const FpG& x, int y) { return x != FpG(y); }

  friend istream& operator>> (istream& is, FpG& t) {
    INT x; is >> x;
    t = x;
    return is;
  }

  friend ostream& operator<< (ostream& os, const FpG& t) {
    os << t.val;
    return os;
  }

};
template<int mod, typename INT>
INT FpG<mod, INT>::dyn_mod;

template<typename T>
class Comb {
  int nMax;
  vector<T> vFact;
  vector<T> vInvFact;
public:
  Comb(int nm) : nMax(nm), vFact(nm+1), vInvFact(nm+1) {
    vFact[0] = 1;
    for (int i = 1; i <= nMax; i++) vFact[i] = i * vFact[i-1];
    vInvFact.at(nMax) = (T)1 / vFact[nMax];
    for (int i = nMax; i >= 1; i--) vInvFact[i-1] = i * vInvFact[i];
  }
  T fact(int n) { return vFact[n]; }
  T inv_fact(int n) { return vInvFact[n]; }
  T binom(int n, int r) {
    if (r < 0 || r > n) return (T)0;
    return vFact[n] * vInvFact[r] * vInvFact[n-r];
  }
  T binom_dup(int n, int r) { return binom(n + r - 1, r); }
  // The number of permutation extracting r from n.
  T perm(int n, int r) {
    return vFact[n] * vInvFact[n-r];
  }
};

constexpr int primeA = 1'000'000'007;
constexpr int primeB = 998'244'353;          // '
using FpA = FpG<primeA, ll>;
using FpB = FpG<primeB, ll>;

// ---- end mod.cc

// ---- inserted function f:<< from util.cc

// declarations

template <typename T1, typename T2>
ostream& operator<< (ostream& os, const pair<T1,T2>& p);

template <typename T1, typename T2, typename T3>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3>& t);

template <typename T1, typename T2, typename T3, typename T4>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4>& t);

template <typename T1, typename T2, typename T3, typename T4, typename T5>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5>& t);

template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5,T6>& t);

template <typename T>
ostream& operator<< (ostream& os, const vector<T>& v);

template <typename T, size_t N>
ostream& operator<< (ostream& os, const array<T, N>& v);

template <typename T, typename C>
ostream& operator<< (ostream& os, const set<T, C>& v);

template <typename T, typename C>
ostream& operator<< (ostream& os, const unordered_set<T, C>& v);

template <typename T, typename C>
ostream& operator<< (ostream& os, const multiset<T, C>& v);

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const map<T1, T2, C>& mp);

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const unordered_map<T1, T2, C>& mp);

template <typename T, typename T2>
ostream& operator<< (ostream& os, const queue<T, T2>& orig);

template <typename T, typename T2>
ostream& operator<< (ostream& os, const deque<T, T2>& orig);

template <typename T, typename T2, typename T3>
ostream& operator<< (ostream& os, const priority_queue<T, T2, T3>& orig);

template <typename T>
ostream& operator<< (ostream& os, const stack<T>& st);

#if __cplusplus >= 201703L
template <typename T>
ostream& operator<< (ostream& os, const optional<T>& t);
#endif

ostream& operator<< (ostream& os, int8_t x);

ostream& operator<< (ostream& os, const __int128& x);

// definitions

template <typename T1, typename T2>
ostream& operator<< (ostream& os, const pair<T1,T2>& p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}

template <typename T1, typename T2, typename T3>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ")";
  return os;
}

template <typename T1, typename T2, typename T3, typename T4>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ", " << get<3>(t) << ")";
  return os;
}

template <typename T1, typename T2, typename T3, typename T4, typename T5>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ", " << get<3>(t) << ", " << get<4>(t) << ")";
  return os;
}

template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
ostream& operator<< (ostream& os, const tuple<T1,T2,T3,T4,T5,T6>& t) {
  os << "(" << get<0>(t) << ", " << get<1>(t)
     << ", " << get<2>(t) << ", " << get<3>(t) << ", " << get<4>(t) << ", " << get<5>(t) << ")";
  return os;
}

template <typename T>
ostream& operator<< (ostream& os, const vector<T>& v) {
  os << '[';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << ']';

  return os;
}

template <typename T, size_t N>
ostream& operator<< (ostream& os, const array<T, N>& v) {
  os << '[';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << ']';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const set<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const unordered_set<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T, typename C>
ostream& operator<< (ostream& os, const multiset<T, C>& v) {
  os << '{';
  for (auto it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  os << '}';

  return os;
}

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const map<T1, T2, C>& mp) {
  os << '[';
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (it != mp.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  os << ']';

  return os;
}

template <typename T1, typename T2, typename C>
ostream& operator<< (ostream& os, const unordered_map<T1, T2, C>& mp) {
  os << '[';
  for (auto it = mp.begin(); it != mp.end(); it++) {
    if (it != mp.begin()) os << ", ";
    os << it->first << ": " << it->second;
  }
  os << ']';

  return os;
}

template <typename T, typename T2>
ostream& operator<< (ostream& os, const queue<T, T2>& orig) {
  queue<T, T2> que(orig);
  bool first = true;
  os << '[';
  while (!que.empty()) {
    T x = que.front(); que.pop();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T, typename T2>
ostream& operator<< (ostream& os, const deque<T, T2>& orig) {
  deque<T, T2> que(orig);
  bool first = true;
  os << '[';
  while (!que.empty()) {
    T x = que.front(); que.pop_front();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T, typename T2, typename T3>
ostream& operator<< (ostream& os, const priority_queue<T, T2, T3>& orig) {
  priority_queue<T, T2, T3> pq(orig);
  bool first = true;
  os << '[';
  while (!pq.empty()) {
    T x = pq.top(); pq.pop();
    if (!first) os << ", ";
    os << x;
    first = false;
  }
  return os << ']';
}

template <typename T>
ostream& operator<< (ostream& os, const stack<T>& st) {
  stack<T> tmp(st);
  os << '[';
  bool first = true;
  while (!tmp.empty()) {
    T& t = tmp.top();
    if (first) first = false;
    else os << ", ";
    os << t;
    tmp.pop();
  }
  os << ']';
  return os;
}

#if __cplusplus >= 201703L
template <typename T>
ostream& operator<< (ostream& os, const optional<T>& t) {
  if (t.has_value()) os << "v(" << t.value() << ")";
  else               os << "nullopt";
  return os;
}
#endif

ostream& operator<< (ostream& os, int8_t x) {
  os << (int32_t)x;
  return os;
}

// for Enum type; just displays ordinals.
template <typename E>
typename std::enable_if<std::is_enum<E>::value, std::ostream&>::type
operator<<(std::ostream& os, E e) {
    return os << static_cast<typename std::underlying_type<E>::type>(e);
}

// This is a very ad-hoc implementation...
// Known problem: "1 << 127" cannot be handled.
ostream& operator<<(ostream& os, const __int128& v) {
  unsigned __int128 a = v < 0 ? -v : v;
  ll i = 0;
  string s(64, ' ');
  if (v == 0) {
    s[i++] = '0';
  }else {
    while (a > 0) {
      s[i++] = '0' + (char)(a % 10);
      a /= 10;
    }
  }
  if (v < 0) {
    s[i++] = '-';
  }
  s.erase(s.begin() + i, s.end());
  reverse(s.begin(), s.end());
  os << s;
  return os;
}

// If a struct has member function "string show() const", operator<< is defined.
template<typename T>
concept HasShow = requires(const T& t) {
  { t.show() } -> same_as<string>;
};
template<HasShow T>
ostream& operator<<(ostream& os, const T& t) {
  return os << t.show();
}

// ---- end f:<<

// ---- inserted library file debug.cc
// published at https://github.com/yamate11/compprog-clib/blob/master/debug.cc
// https://github.com/yamate11/compprog-clib/blob/master/debug.cc

template <class... Args>
string dbgFormat(const char* fmt, Args... args) {
  size_t len = snprintf(nullptr, 0, fmt, args...);
  char buf[len + 1];
  snprintf(buf, len + 1, fmt, args...);
  return string(buf);
}

template <class Head>
void dbgLog(bool with_nl, Head&& head) {
  cerr << head;
  if (with_nl) cerr << endl;
}

template <class Head, class... Tail>
void dbgLog(bool with_nl, Head&& head, Tail&&... tail)
{
  cerr << head << " ";
  dbgLog(with_nl, forward<Tail>(tail)...);
}

#if DEBUG
  #define DLOG(...)        dbgLog(true, __VA_ARGS__)
  #define DLOGNNL(...)     dbgLog(false, __VA_ARGS__)
  #define DFMT(...)        cerr << dbgFormat(__VA_ARGS__) << endl
  #define DCALL(func, ...) func(__VA_ARGS__)
#else
  #define DLOG(...)
  #define DLOGNNL(...)
  #define DFMT(...)
  #define DCALL(func, ...)
#endif

/*
#if DEBUG_LIB
  #define DLOG_LIB(...)        dbgLog(true, __VA_ARGS__)
  #define DLOGNNL_LIB(...)     dbgLog(false, __VA_ARGS__)
  #define DFMT_LIB(...)        cerr << dbgFormat(__VA_ARGS__) << endl
  #define DCALL_LIB(func, ...) func(__VA_ARGS__)
#else
  #define DLOG_LIB(...)
  #define DFMT_LIB(...)
  #define DCALL_LIB(func, ...)
#endif
*/

#define DUP1(E1)       #E1 "=", E1
#define DUP2(E1,E2)    DUP1(E1), DUP1(E2)
#define DUP3(E1,...)   DUP1(E1), DUP2(__VA_ARGS__)
#define DUP4(E1,...)   DUP1(E1), DUP3(__VA_ARGS__)
#define DUP5(E1,...)   DUP1(E1), DUP4(__VA_ARGS__)
#define DUP6(E1,...)   DUP1(E1), DUP5(__VA_ARGS__)
#define DUP7(E1,...)   DUP1(E1), DUP6(__VA_ARGS__)
#define DUP8(E1,...)   DUP1(E1), DUP7(__VA_ARGS__)
#define DUP9(E1,...)   DUP1(E1), DUP8(__VA_ARGS__)
#define DUP10(E1,...)   DUP1(E1), DUP9(__VA_ARGS__)
#define DUP11(E1,...)   DUP1(E1), DUP10(__VA_ARGS__)
#define DUP12(E1,...)   DUP1(E1), DUP11(__VA_ARGS__)
#define GET_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,_11,_12,NAME,...) NAME
#define DUP(...)          GET_MACRO(__VA_ARGS__, DUP12, DUP11, DUP10, DUP9, DUP8, DUP7, DUP6, DUP5, DUP4, DUP3, DUP2, DUP1)(__VA_ARGS__)
#define DLOGK(...)        DLOG(DUP(__VA_ARGS__))
#define DLOGKL(lab, ...)  DLOG(lab, DUP(__VA_ARGS__))

#if DEBUG_LIB
  #define DLOG_LIB   DLOG
  #define DLOGK_LIB  DLOGK
  #define DLOGKL_LIB DLOGKL
#endif

// ---- end debug.cc

// ---- inserted library file cmpNaive.cc
// published at https://github.com/yamate11/compprog-clib/blob/master/cmpNaive.cc

const string end_mark("^__=end=__^");

int naive(istream& cin, ostream& cout);
int body(istream& cin, ostream& cout);

void cmpNaive() {
  while (true) {
    string s;
    getline(cin, s);
    bool run_body;
    if (s.at(0) == 'Q') {
      return;
    }else if (s.at(0) == 'B') {
      run_body = true;
    }else if (s.at(0) == 'N') {
      run_body = false;
    }else {
      cerr << "Unknown body/naive specifier.\n";
      exit(1);
    }
    string input_s;
    while (true) {
      getline(cin, s);
      if (s == end_mark) break;
      input_s += s;
      input_s += "\n";
    }
    stringstream ss_in(move(input_s));
    stringstream ss_out;
    ss_out << setprecision(20);
    if (run_body) {
      body(ss_in, ss_out);
    }else {
      naive(ss_in, ss_out);
    }
    cout << ss_out.str() << end_mark << endl;
  }
}

int main(int argc, char *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << setprecision(20);

#if CMPNAIVE
  if (argc == 2) {
    if (strcmp(argv[1], "cmpNaive") == 0) {
      cmpNaive();
    }else if (strcmp(argv[1], "naive") == 0) {
      naive(cin, cout);
    }else if (strcmp(argv[1], "skip") == 0) {
      exit(0);
    }else {
      cerr << "Unknown argument.\n";
      exit(1);
    }
  }else {
#endif
    body(cin, cout);
#if CMPNAIVE
  }
#endif
  return 0;
}

/*
int naive(istream& cin, ostream& cout) {
  return 0;
}
int body(istream& cin, ostream& cout) {
  return 0;
}
*/

// ---- end cmpNaive.cc

// @@ !! LIM -- end mark --

using Fp = FpB;

int naive(istream& cin, ostream& cout) {
  ll N, Q; cin >> N >> Q;
  // @InpVec(N, A) [QQ0TOsp4]
  auto A = vector(N, ll());
  for (int i = 0; i < N; i++) { ll v; cin >> v; A[i] = v; }
  // @End [QQ0TOsp4]
  ranges::sort(A);
  A.erase(unique(ALL(A)), A.end());
  N = ssize(A);

  REP(_q, 0, Q) {
    ll k, x, m; cin >> k >> x >> m; x--;
    REP(kk, 0, k) {
      ll t = A[0] + 1;
      vector<ll> newA;
      ll idx = 1;
      while (true) {
        if (idx < ssize(A) and A[idx] == t) {
          idx++;
        }else {
          newA.push_back(t);
          if (ssize(newA) == m) break;
        }
        t++;
      }
      A = move(newA);
    }
    DLOGK(_q, A);
    cout << A[x] << "\n";
  }


  return 0;
}
int body(istream& cin, ostream& cout) {

  ll N, Q; cin >> N >> Q;
  // @InpVec(N, A) [QQ0TOsp4]
  auto A = vector(N, ll());
  for (int i = 0; i < N; i++) { ll v; cin >> v; A[i] = v; }
  // @End [QQ0TOsp4]
  ranges::sort(A);
  A.erase(unique(ALL(A)), A.end());
  N = ssize(A);

  auto fsub = [&](auto& B, ll m) -> ll {
    assert(ssize(B) % 2 != 0);
    ll ret = B[0];
    auto old_B = move(B);
    B = vector<ll>();
    ll i = 1;
    while (true) {
      if (i < ssize(old_B) and old_B[i] < m) {
        B.push_back(old_B[i]);
        B.push_back(old_B[i + 1]);
        m -= old_B[i];
        i += 2;
      }else {
        B.push_back(m);
        break;
      }
    }
    assert(ssize(B) % 2 != 0);
    return ret;
  };

  auto func = [&](Fp top, auto& B, ll k, ll m) -> Fp {
    top += fsub(B, m);
    DLOGKL("  1", top, B);
    if (k == 1) return top;
    top += fsub(B, m);
    DLOGKL("  2", top, B);
    if (k == 2) return top;
    top += fsub(B, m);
    DLOGKL("  3", top, B);
    if (k == 3) return top;
    top += fsub(B, m);
    DLOGKL("  4", top, B);
    if (k == 4) return top;
    k -= 4;
    ll t = 0;
    ll sz = ssize(B);
    assert(sz % 2 != 0);
    for (ll i = 1; i < sz; i += 2) t += B[i];
    B.push_back(m - t);
    ll p = k / (sz + 1);
    ll q = k % (sz + 1);
    top += 2 * m * p;
    REP(i, 0, q) top += B[i];
    auto old_B = move(B);
    B = vector<ll>(sz + 1);
    REP(i, 0, sz + 1) B[i] = old_B[(i + q) % (sz + 1)];
    B.pop_back();
    assert(ssize(B) % 2 != 0);
    return top;
  };

  Fp top = A[0];
  vector<ll> B;
  {
    ll st = 0;
    while (true) {
      ll i = 0;
      while (st + i < N and A[st + i] == A[st] + i) i++;
      B.push_back(i);
      if (st + i == N) break;
      B.push_back(A[st + i] - A[st + (i - 1)] - 1);
      st = st + i;
    }
  }
  DLOGK(N, B);
  assert(ssize(B) % 2 != 0);
  REP(_q, 0, Q) {
    ll k, x, m; cin >> k >> x >> m; x--;
    top = func(top, B, k, m);
    DLOGK(_q, top, B);
    assert(ssize(B) % 2 != 0);
    Fp cur = top;
    for (ll i = 0; i < ssize(B); i += 2) {
      if (x < B[i]) {
        cout << cur + x << "\n";
        break;
      }
      cur += B[i] + B[i + 1];
      x -= B[i];
    }
  }

  return 0;
}