#1192663 (C++23) No.3756 Udon Network

• 問題: No.3756 Udon Network
• ユーザー: miscalc
• 提出日時: 2026-10-10 00:44:34
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: TLE
• 実行時間: -
• コード長: 47,252 bytes
• コンパイル時間: 3,881 ms
• コンパイル使用メモリ: 390,352 KB
• 実行使用メモリ: 120,492 KB
• 最終ジャッジ日時: 2026-10-10 00:45:59
• 合計ジャッジ時間: 73,900 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge3_1

サブタスク	配点	結果
Example	0 %	AC * 8
Subtask $1$	2 %	AC * 15
Subtask $2$	4 %	AC * 22
Subtask $3$	8 %	AC * 5 TLE * 4
Subtask $4$	16 %	AC * 7 TLE * 3
Subtask $5$	32 %	AC * 7 TLE * 3
Subtask $6$	38 %	AC * 37 TLE * 16
合計	4 * 6% = 24 点

ソースコード

#define SINGLE_TESTCASE 
// #define MULTI_TESTCASE
// #define AOJ_TESTCASE

#define FAST_IO 
// #define FAST_CIO
// #define INTERACTIVE

#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11

// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp

#include <bits/stdc++.h>
using namespace std;

using ld = decltype(EPS);

using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;

#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;

using vb = vc<bool>;
using vl = vc<ll>;
using vpll = vc<pll>;
using vtlll = vc<tlll>;
using vtllll = vc<tllll>;
using vstr = vc<string>;
using vvb = vvc<bool>;
using vvl = vvc<ll>;

template <class T>
using pql = priority_queue<T, vc<T>, greater<T>>;
template <class T>
using pqg = priority_queue<T>;

using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
  const bool neg = s.front() == '-';
  u128 res = 0;
  for (int i = neg; i < (int)s.size(); i++)
    res = 10 * res + s[i] - '0';
  if (neg)
    return -i128(res - 1) - 1;
  return i128(res);
}
string i128tos(i128 x)
{
  if (x == 0) return "0";
  string sign = "", res = "";
  u128 ux;
  if (x < 0)
    ux = u128(-(x + 1)) + 1, sign = "-";
  else
    ux = x;
  while (ux > 0)
  {
    res += '0' + ux % 10;
    ux /= 10;
  }
  reverse(res.begin(), res.end());
  return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
  string s;
  is >> s;
  a = stoi128(s);
  return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
  os << i128tos(a);
  return os;
}

#define cauto const auto
// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp

#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(i,n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep2(i,l,r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)
#define rep3(i,l,r,d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i,l,r,d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)

#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp

template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;

template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;

template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
// https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp

namespace default_infty_detail
{
  template <class T, class = void>
  struct has_infty : false_type {};

  template <class T>
  struct has_infty<T, void_t<decltype(T::infty())>> : true_type {};

  template <class T>
  inline constexpr bool unsupported = false;
}

template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divround(U a, V b) { return divfloor<T>(2 * T(a) + T(b), 2 * T(b)); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }

// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp

#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back

#define LMD(x,fx) ([&](const auto &x) { return fx; })
#define GEN_VEC(n,i,fi) (gen_vec(n, LMD(i, fi)))

template <class V, class T>
void fill(V &v, const T &value)
{
  if constexpr (is_assignable_v<decltype(*std::begin(v)), const T &>)
    std::fill(std::begin(v), std::end(v), value);
  else
    for (auto &row : v) fill(row, value);
}

// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp

template <class V, class Equal = equal_to<>>
void unique(V &v, Equal equal = {}) { v.erase(std::unique(ALL(v), equal), v.end()); }

template <class V, class Compare = less<>, class Equal = equal_to<>>
void sortunique(V &v, Compare comp = {}, Equal equal = {})
{
  sort(ALL(v), comp);
  unique(v, equal);
}
template <class V, class Compare = less<>, class Equal = equal_to<>>
V sortuniqued(V v, Compare comp = {}, Equal equal = {})
{ sortunique(v, comp, equal); return v; }

template <class T>
vvc<T> top(const vvc<T> &a)
{
  if (a.empty())
    return {};
  const int n = a.size(), m = a[0].size();
  vvc<T> b(m, vc<T>(n));
  repi(i, n)
  {
    assert(SZ<int>(a[i]) == m);
    repi(j, m) b[j][i] = a[i][j];
  }
  return b;
}
vstr top(const vstr &a)
{
  vvc<char> a_(a.size());
  repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
  vvc<char> b_ = top(a_);
  vstr b(b_.size());
  repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
  return b;
}

template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;

template <class T>
struct MonoidAdd
{
  using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMin
{
  using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMax
{
  using S = T;
};

namespace internal
{
  template <class M, class I, class = void>
  struct HasMonoidPow : false_type
  {
  };
  template <class M, class I>
  struct HasMonoidPow<M, I, void_t<decltype(M::pow(declval<const typename M::S &>(), declval<I>()))>> : true_type
  {
  };
}

constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp

template <class T>
struct is_random_access_iterator
{
  static constexpr bool value = is_same_v<
    typename iterator_traits<T>::iterator_category,
    random_access_iterator_tag
  >;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;

#define DEFAULT_COMP ranges::less

namespace internal
{
template <class T>
bool binsearch_adjacent(T a, T b)
{
  if (a < b)
    return a + 1 == b;
  if (b < a)
    return b + 1 == a;
  return false;
}
};

// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp

template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }

inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }

inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }

inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }

inline constexpr ull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }
inline constexpr ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }
inline constexpr ull lsb_mask(ull x) { assert(x != 0); return x & -x; }
inline constexpr ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }

inline constexpr bool btest(ull x, uint k) { return (x >> k) & 1; }
inline constexpr bool bsubset(ull x, ull y) { return (x & y) == x; }
inline constexpr bool bsupset(ull x, ull y) { return (x & y) == y; }
inline constexpr ull bsetminus(ull x, ull y) { return x & ~y; }
// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp

// https://github.com/miscalculation53/library/tree/wip/template/template_dump_map.hpp

#define CPP_DUMP_DEFINE_DATA(...) 
#define dump(...) ((void)0)
#define local(...) 
#define oj(...) __VA_ARGS__
#define local_oj(a,b) (b)

template <class T, class Sequence>
vc<T> content(queue<T, Sequence> que);
template <class T, class Sequence, class Compare>
vc<T> content(priority_queue<T, Sequence, Compare> pque);
template <class T>
auto content(const T &obj);

namespace fastio {
template <class T>
struct unsigned_integer
{
  using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128>
{
  using type = u128;
};
template <>
struct unsigned_integer<u128>
{
  using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;

static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
  pil = 0;
  if (pir < SIZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd1(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (c <= ' ');
}

void rd1(string &x) {
  x.clear();
  while (true) {
    if (pil == pir) load();
    while (pil < pir && ibuf[pil] <= ' ') ++pil;
    if (pil < pir) break;
  }
  while (true) {
    uint32_t p = pil;
    while (pil < pir && ibuf[pil] > ' ') ++pil;
    x.append(ibuf + p, pil - p);
    if (pil < pir) {
      ++pil;
      return;
    }
    load();
  }
}

template <typename T>
void rd1_real(T &x) {
  string s;
  rd1(s);

  if constexpr (!is_same_v<T, long double>)
  {
    auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
    if (ec == errc{} && p == s.data() + s.size()) return;
  }

  if constexpr (is_same_v<T, long double>)
    x = stold(s);
  else
    x = stod(s);
}

template <bool check_buffer = true, typename T>
void rd1_integer(T &x) {
  using U = unsigned_integer_t<T>;
  bool minus = false;
  U val = 0;
  if constexpr (check_buffer)
    if (pil + 100 > pir) load();
  uint32_t p = pil;
  while (ibuf[p] < '-') ++p;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (ibuf[p] == '-') minus = true, ++p;
  }
  while ('0' <= ibuf[p]) val = val * 10 + (ibuf[p++] & 15);
  pil = p;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>)
  {
    if (minus)
    {
      const U min_abs = U(numeric_limits<T>::max()) + 1;
      x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
    }
    else x = T(val);
  }
  else
    x = T(val);
}

void rd1(int &x) { rd1_integer(x); }
void rd1(ll &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
void rd1(ull &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }

template <class T, class U>
void rd1(pair<T, U> &p) {
  return rd1(p.first), rd1(p.second);
}
template <class... T>
void rd1(tuple<T...> &tpl) {
  apply([](auto &...x) { (rd1(x), ...); }, tpl);
}

template <class T>
void rd1(vc<T> &x) {
  for (auto &d: x) rd1(d);
}

template <class... T>
void read(T &...x) {
  if constexpr (sizeof...(T) <= SIZ / 100 &&
                ((!is_same_v<T, char> &&
                  (is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>)) && ...)) {
    if (pil + 100 * sizeof...(T) > pir) load();
    (rd1_integer<false>(x), ...);
  }
  else
    (rd1(x), ...);
}

void wt1(const char c) {
  if (por == SIZ) flush();
  obuf[por++] = c;
}
void wt1(string_view s) {
  while (!s.empty()) {
    if (por == SIZ) flush();
    size_t n = min<size_t>(s.size(), SIZ - por);
    memcpy(obuf + por, s.data(), n);
    por += n;
    s.remove_prefix(n);
  }
}

template <typename T>
void wt1_integer(T x) {
  if (por > SIZ - 100) flush();
  using U = unsigned_integer_t<T>;
  U ux;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>)
  {
    if (x < 0)
      obuf[por++] = '-', ux = U(0) - U(x);
    else
      ux = U(x);
  }
  else
    ux = x;
  int outi;
  for (outi = 96; ux >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[ux % 10000], 4);
    ux /= 10000;
  }
  if (ux >= 1000) {
    memcpy(obuf + por, pre.num[ux], 4);
    por += 4;
  } else if (ux >= 100) {
    memcpy(obuf + por, pre.num[ux] + 1, 3);
    por += 3;
  } else if (ux >= 10) {
    int q = (ux * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (ux - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = ux | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt1_real(T x) {

  if constexpr (!is_same_v<T, long double>)
  {
    auto [p, ec] = to_chars(out, out + sizeof(out), x, chars_format::fixed, 15);
    if (ec == errc{}) {
      wt1(string_view(out, p));
      return;
    }
  }

  ostringstream oss;
  oss << fixed << setprecision(15) << x;
  wt1(oss.str());
}

void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }

template <class... T>
void write(T &&...x) {
  (wt1(std::forward<T>(x)), ...);
}

template <class... T>
void print(T &&...x) {
  if constexpr (sizeof...(T))
  {
    int i = 0;
    ((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
  }
  wt1('\n');
}

} 

struct Dummy {
  Dummy() { atexit(fastio::flush); }
} dummy;

namespace internal
{

template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }

template <class... T>
void READVECnodump(int n, vc<T> &...v)
{
  (v.resize(n), ...);
  READnodump(v...);
}

}; 

#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)

#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)

#define CHAR(...) IN(char, __VA_ARGS__)
#define INT(...) IN(int, __VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define STR(...) IN(string, __VA_ARGS__)
#define ARR(T,n,...) array<T, n> __VA_ARGS__; READ(__VA_ARGS__)

#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)

#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T,n,m,...) vvc<T> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)

#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)

#define JAG(T,n,...) vvc<T> __VA_ARGS__; READJAG(n, __VA_ARGS__)

#define ENDL '\n'

#define WRITE fastio::write
#define PRINT fastio::print

#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)
#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)

template <class T>
void PRINTV(const vc<T> &v) { for (auto &vi : v) PRINT(vi); }
#define PRINTVEXIT(...) do { PRINTV(__VA_ARGS__); exit(0); } while (false)
#define PRINTVRETURN(...) do { PRINTV(__VA_ARGS__); return; } while (false)

template <class T, class U, class P>
pair<T, U> &operator+=(pair<T, U> &a, const P &b)
{
  a.first += b.first;
  a.second += b.second;
  return a;
}

namespace internal
{

template <size_t... I, class A, class B>
auto &tuple_add_impl(A &a, const B &b, const index_sequence<I...>)
{
  ((get<I>(a) += get<I>(b)), ...);
  return a;
}

}; 

template <class... Ts, class Tp>
tuple<Ts...> &operator+=(tuple<Ts...> &a, const Tp &b)
{ return internal::tuple_add_impl(a, b, make_index_sequence<tuple_size_v<tuple<Ts...>>>{}); }

template <class T, class Add>
void offset(vc<T> &v, const Add &add) { for (auto &vi : v) vi += add; }

template <class T, const size_t m>
array<vc<T>, m> unzip(const vc<array<T, m>> &vt)
{
  const size_t n = vt.size();
  array<vc<T>, m> tv;
  tv.fill(vc<T>(n));
  for (size_t i = 0; i < n; i++)
    for (size_t j = 0; j < m; j++)
      tv[j][i] = vt[i][j];
  return tv;
}

template <class T, class U>
pair<vc<T>, vc<U>> unzip(const vc<pair<T, U>> &vt)
{
  const size_t n = vt.size();
  pair<vc<T>, vc<U>> tv;
  tv.first.resize(n), tv.second.resize(n);
  for (size_t i = 0; i < n; i++)
    tie(tv.first[i], tv.second[i]) = vt[i];
  return tv;
}

namespace internal
{

template <size_t... I, class V, class Tp>
auto vt_to_tv_impl(V &tv, const Tp &t, index_sequence<I...>, size_t index)
{ ((get<I>(tv)[index] = get<I>(t)), ...); }

};

template <class... Ts>
auto unzip(const vc<tuple<Ts...>> &vt)
{
  const size_t n = vt.size();
  tuple<vc<Ts>...> tv;
  apply([&](auto &...v)
        { ((v.resize(n)), ...); }, tv);
  for (size_t i = 0; i < n; i++)
    internal::vt_to_tv_impl(tv, vt[i], make_index_sequence<tuple_size_v<decltype(tv)>>{}, i);
  return tv;
}

namespace internal
{

};

#define UNZIP(vt,...) auto [__VA_ARGS__] = unzip(vt)
#define ZIP(vt,...) auto vt = internal::zip_vectors(__VA_ARGS__)

// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp

mt19937_64 mt;

bool randbool(double p)
{
  assert(0 <= p && p <= 1);
  return bernoulli_distribution(p)(mt);
}

namespace internal
{
}; 

// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp

// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp

namespace larger_int_detail
{
}

template <class T>
struct larger_int
{
private:
  static constexpr bool check();
  static_assert(check());

public:
  using type = T;
};

#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };

LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)

LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)

#undef LARGER_INT

template <class T>
struct Rational;

template <class T>
struct larger_int<Rational<T>>
{
  using type = Rational<typename larger_int<T>::type>;
};

template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp

namespace internal
{

template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
  if (m == 1)
    return 0;
  using U = make_unsigned_t<T>;
  using L = larger_int_t<U>;

  U r = 1, y = safemod(x, m);
  while (n)
  {
    if (n & 1)
      r = L(r) * y % m;
    y = L(y) * y % m;
    n >>= 1;
  }
  return r;
}

template <auto n>
constexpr bool isprime = isprime_constexpr(n);

};

namespace internal
{

template <auto M>
struct policy_static
{
  using mod_type = decltype(M);
  using value_type = make_unsigned_t<mod_type>;
  using calc_type = conditional_t<(M <= UINT_MAX), ull, larger_int_t<value_type>>;

  static constexpr bool is_prime = isprime_constexpr(M);

  static constexpr mod_type mod() { return M; }
  static constexpr value_type umod() { return M; }

  static constexpr value_type init(value_type v) { return v; }
  static constexpr mod_type val(value_type v) { return v; }
};

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp

namespace internal
{

struct barrett32
{
  uint m = 0;
  ull im = 0;
  barrett32() = default;
  explicit barrett32(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((u128(z) * im) >> 64);
    ull y = x * m;
    return uint(z - y + (z < y ? m : 0));
  }
};

template <int id>
struct policy_barrett32
{
  using value_type = uint;
  using calc_type = ull;
  using mod_type = int;
  
  static constexpr bool is_prime = false;
  static inline barrett32 reducer{};
  static void set_mod(mod_type m)
  {
    assert(m >= 1 && "modint: set_mod(m) requires m >= 1");
    reducer = barrett32(m);
  }
  static mod_type mod() { return reducer.umod(); }
  static value_type umod() { return reducer.umod(); }
  static value_type init(value_type v) { return v; }
  static mod_type val(value_type v) { return v; }
};

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp

namespace internal
{

inline constexpr ull inv64(ull a)
{
  ull x = a;
  while (a * x != 1) x *= 2 - a * x;
  return x;
}

struct montgomery64odd
{
  ull m = 0, im = 0, sq = 0;
  montgomery64odd() = default;
  explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
  ull umod() const { return m; }
  ull reduce(u128 x) const
  {
    auto t = (x + u128(m) * (-im * ull(x))) >> 64;
    if (t >= m) t -= m;
    return (ull)t;
  }
  ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};

struct montgomery64
{
  ull m = 0, mx = 0, imx = 0, d = 0, q = 0;
  uint b = 0;
  montgomery64() = default;
  explicit montgomery64(ull m) : m(m)
  {
    b = countr_zero(m), mx = m >> b; 
    imx = inv64(mx);
    d = powmod_constexpr((mx + 1) / 2, b, mx); 
    u128 sq = -u128(mx) % mx; 
    q = (1 + (((sq - 1) * d) << b)) % m;
  }
  ull umod() const { return m; }
  ull reduce(u128 x) const
  {
    if (b == 0)
    {
      auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
      if (t >= m) t -= m;
      return (ull)t;
    }
    ull p = x & MASK(b); 
    x = (x >> b) + p * d;
    ull y = p << (64 - b);
    auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
    if (t >= m) { t -= m; if (t >= m) t -= m; }
    return (ull)t;
  }
  ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};

template <int id>
struct policy_montgomery64_odd
{
  using value_type = ull;
  using calc_type = u128;
  using mod_type = ll;

  static constexpr bool is_prime = false;
  static inline montgomery64odd reducer{};
  static void set_mod(mod_type m)
  {
    assert(m >= 1 && m % 2 == 1 && "modint: set_mod(m) requires a positive odd modulus");
    reducer = montgomery64odd(m);
  }
  static mod_type mod() { return reducer.umod(); }
  static value_type umod() { return reducer.umod(); }
  static value_type init(value_type v) { return reducer.inv_reduce(v); }
  static mod_type val(value_type v) { return reducer.reduce(v); }
};

template <int id>
struct policy_montgomery64
{
  using value_type = ull;
  using calc_type = u128;
  using mod_type = ll;

  static constexpr bool is_prime = false;
  static inline montgomery64 reducer{};
  static void set_mod(mod_type m)
  {
    assert(m >= 1 && "modint: set_mod(m) requires m >= 1");
    reducer = montgomery64(m);
  }
  static mod_type mod() { return reducer.umod(); }
  static value_type umod() { return reducer.umod(); }
  static value_type init(value_type v) { return reducer.inv_reduce(v); }
  static mod_type val(value_type v) { return reducer.reduce(v); }
};

};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp

namespace internal
{

  template <class Policy, class PowInv = void>
  struct modint_impl
  {
    using V = typename Policy::value_type;
    using M = typename Policy::mod_type;
    using mint = modint_impl;

  private:
    V _v;

  public:
    static constexpr M mod()
    {
      M m = Policy::mod();
      assert(m > 0 && "modint: modulus is not set; call mint::set_mod(m) before use");
      return m;
    }

    template <class T = Policy>
    static auto set_mod(M m) -> decltype(T::set_mod(m)) { return T::set_mod(m); }

    M val() const { return Policy::val(_v); }

    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 M safe_hash_key(const mint &x) { return x.val(); }
  
    friend void rd1(mint &x)
    {
      long long a;
      fastio::rd1(a);
      x = a;
    }
    friend void wt1(const mint &x)
    {
      fastio::wt1(x.val());
    }

  };

};

template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;

using modint998244353 = static_modint32<998244353>;
using modint1000000007 = static_modint32<1000000007>;
using modint = dynamic_modint32<-1>;
using modint61 = static_modint64<(1LL << 61) - 1>;
using modint64 = dynamic_modint64<-1>;

template <class T>
struct is_modint : std::false_type
{
};
template <class Policy, class PowInv>
struct is_modint<internal::modint_impl<Policy, PowInv>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;

template <class T>
struct is_static_modint : false_type {};
template <int m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <ll m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;

template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;

template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};

template <class mint>
struct modint_less
{
  bool operator()(const mint &a, const mint &b) const
  {
    if constexpr (is_modint_v<mint>)
      return a.val() < b.val();
    else
      return a < b;
  }
};

template <class mint>
struct modint_hash
{
  auto operator()(const mint &x) const
  {
    if constexpr (is_modint_v<mint>)
      return std::hash<decltype(x.val())>{}(x.val());
    else
      return std::hash<mint>{}(x);
  }
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp

template <class mint>
struct PowerTable
{
private:
  decltype(mint::mod()) mod;
  mint base;
  vc<mint> pw;

public:

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp

template <class T>
struct Binomial
{
private:
  inline static decltype(T::mod()) mod;
  
public:
  inline static vc<T> fac_, finv_, inv_;

};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp

// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp

// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp

template <class T = ll, class U = larger_int_t<T>>
pair<T, T> svp2d(const pair<T, T> &a, const pair<T, T> &b)
{
  assert((a != pair<T, T>{0, 0} && b != pair<T, T>{0, 0}));
  auto [a1, a2] = a;
  auto [b1, b2] = b;
  if constexpr (is_same_v<U, i128> && is_integral_v<T> && is_signed_v<T> && sizeof(T) <= sizeof(ll))
  {
    
    constexpr ull offset = 1ULL << 30;
    if (((ull(a1) + offset) |
         (ull(a2) + offset) |
         (ull(b1) + offset) |
         (ull(b2) + offset)) < 2 * offset)
      return svp2d<T, ll>(a, b);
  }
  if ((U)a1 * a1 + (U)a2 * a2 < (U)b1 * b1 + (U)b2 * b2)
    swap(a1, b1), swap(a2, b2);
  while ((U)a1 * a1 + (U)a2 * a2 > (U)b1 * b1 + (U)b2 * b2)
  {
    swap(a1, b1), swap(a2, b2);
    T k = divround<U>((U)a1 * b1 + (U)a2 * b2, (U)a1 * a1 + (U)a2 * a2);
    b1 -= k * a1, b2 -= k * a2;
    if (b1 == 0 && b2 == 0)
      return {a1, a2};
  }
  return {a1, a2};
}

template <class mint>
pair<decltype(mint(0).val()), decltype(mint(0).val())>
mint_to_rat(const mint &x)
{
  auto [p, q] = svp2d({x.val(), 1}, {mint::mod(), 0});
  if (q < 0)
    p = -p, q = -q;
  return {p, q};
}

namespace cpp_dump
{
  template <class T>
  struct rat_value
  {
    T p, q;

    friend ostream &operator<<(ostream &os, const rat_value &x)
    {
      os << x.p;
      if (x.q != 1)
        os << '/' << x.q;
      return os;
    }
  };

  struct mint_to_rat_fn
  {
    template <class T>
      requires requires(const T &x)
      {
        { T::mod() } -> std::convertible_to<ll>;
        { x.val() } -> std::convertible_to<ll>;
      }
    constexpr auto operator()(const T &x) const
        -> rat_value<typename decltype(mint_to_rat(x))::first_type>
    {
      auto [p, q] = mint_to_rat(x);
      return {p, q};
    }
  };

  template <class T>
  struct rat_object
  {
    T value;
  };

  template <class T>
  inline constexpr bool rat_is_map = false;
  template <class... Args>
  inline constexpr bool rat_is_map<std::map<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::multimap<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::unordered_map<Args...>> = true;
  template <class... Args>
  inline constexpr bool rat_is_map<std::unordered_multimap<Args...>> = true;

  struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
  {
    template <class T>
    static constexpr bool can_convert()
    {

      if constexpr (std::ranges::range<T>)
      {
        using Ref = std::ranges::range_reference_t<T>;
        if constexpr (std::same_as<std::remove_cvref_t<T>, std::remove_cvref_t<Ref>>)
          return false;
        else
          return can_convert<Ref>();
      }
      else if constexpr (requires { std::tuple_size<std::remove_cvref_t<T>>::value; })
      {
        return []<size_t... I>(std::index_sequence<I...>)
        {
          if constexpr ((requires { std::get<I>(std::declval<T>()); } && ...))
            return (can_convert<decltype(std::get<I>(std::declval<T>()))>() || ...);
          else
            return false;
        }(std::make_index_sequence<std::tuple_size_v<std::remove_cvref_t<T>>>{});
      }
      else
        return std::invocable<mint_to_rat_fn, T>;
    }

    template <typename T>
      requires(!requires { std::views::all | std::declval<T>(); })
    constexpr decltype(auto) operator()(T &&t) const
    {
      if constexpr (!std::ranges::range<T> && std::invocable<mint_to_rat_fn, T>)
      {
        return mint_to_rat_fn{}(std::forward<T>(t));
      }
      else if constexpr (can_convert<T>())
      {

        if constexpr (!std::ranges::range<T> || rat_is_map<std::remove_cvref_t<T>>)
          return rat_object<T>{std::forward<T>(t)};
        else
          return std::forward<T>(t) | std::views::transform(*this);
      }
      else
      {
        return std::forward<T>(t);
      }
    }
  };

  constexpr rat_closure rat()
  {
    return rat_closure{};
  }
}

using mint = modint998244353;
// using mint = modint1000000007;
// using mint = static_modint<1000000000>;
// using mint = modint;
using bi = Binomial<mint>;

void init()
{
  oj(mt.seed(random_device()()));
}

// https://github.com/miscalculation53/library/tree/wip/algo/parallel_binsearch.hpp

template <class T = ll, class Judge, class InitOk, class InitNg>
pair<vc<T>, vc<T>> parallel_binsearch(int q, const Judge &judge, InitOk init_ok, InitNg init_ng, bool check_ok = true, bool check_ng = true)
{
  if (check_ok)
  {
    auto res = judge(vc<T>(q, init_ok));
    assert(all_of(ALL(res), LMD(x, x)));
  }
  if (check_ng)
  {
    auto res = judge(vc<T>(q, init_ng));
    assert(all_of(ALL(res), LMD(x, !x)));
  }
  vc<T> oks(q, init_ok), ngs(q, init_ng);
  while (true)
  {
    vc<T> mids(q);
    bool end = true;
    repi(i, q)
    {
      if (!internal::binsearch_adjacent(oks[i], ngs[i]))
        end = false;
      mids[i] = (oks[i] & ngs[i]) + ((oks[i] ^ ngs[i]) >> 1);
    }
    if (end)
      break;
    auto res = judge(mids);
    repi(i, q) (res[i] ? oks[i] : ngs[i]) = mids[i];
  }
  return {oks, ngs};
}

// https://github.com/miscalculation53/library/tree/wip/ds/uf/uf.hpp

template <class UFData, bool compress = true>
struct UnionFind
{
  friend UFData;

protected:
  vc<int> par;
  vc<typename UFData::VData> vdat;

public:
  typename UFData::GData gdat;

  UnionFind() {}
  UnionFind(int n) : par(n, -1), vdat(n), gdat(n)
  { repi(i, n) vdat[i] = typename UFData::VData(i); }

  virtual int leader(int x)
  {
    assert(0 <= x && x < SZ<int>(par));
    if (par[x] < 0)
      return x;
    if constexpr (compress)
      return par[x] = leader(par[x]);
    else
      return leader(par[x]);
  }
  
  template <class I = ll>
  I size(int x) { return -par[leader(x)]; }
  typename UFData::VData &get_vdata(int x) { return vdat[leader(x)]; }
  
  template <class I = ll>
  I merge(int x, int y, const typename UFData::EWeight &w = 1)
  {
    x = leader(x), y = leader(y);
    if (x == y)
    {
      UFData::add_edge_same(*this, x, w);
      return x;
    }
    if (-par[x] < -par[y])
      swap(x, y);
    par[x] += par[y], par[y] = x;
    UFData::add_edge_diff(*this, x, y, w);
    return x;
  }

};

template <class EWeight_ = ll>
struct UFDataEmpty
{
  struct VData
  {
  };
  struct GData
  {
  };
  using EWeight = EWeight_;
  template <class UF>
  static void add_edge_diff(UF &, int, int, EWeight) {}
  template <class UF>
  static void add_edge_same(UF &, int, EWeight) {}
};

template <class EWeight_ = ll, bool need_vlist = false>
struct UFDataEverything
{
  struct VData
  {

    ll vsum;
    EWeight_ esum;
    vc<ll> vlist;

    // 頂点 i の初期化
  };
  struct GData
  {

    ll cmp_cnt;
    ll min_leader, max_leader;

    // 頂点数 n のグラフの初期化
  };
  using EWeight = EWeight_;
  template <class UF>
  static void add_edge_diff(UF &uf, int x, int y, EWeight w)
  {
    VData &xd = uf.vdat[x], &yd = uf.vdat[y];
    GData &gd = uf.gdat;

    xd.vsum += yd.vsum;
    xd.esum += yd.esum + w;
    if constexpr (need_vlist)
    {
      xd.vlist.insert(xd.vlist.end(), ALL(yd.vlist));
      yd.vlist.clear();
    }
    gd.cmp_cnt--;
    while (uf.leader(gd.min_leader) != gd.min_leader)
      gd.min_leader++;
    while (uf.leader(gd.max_leader) != gd.max_leader)
      gd.max_leader--;
  }
  template <class UF>
  static void add_edge_same(UF &uf, int x, EWeight w)
  {
    VData &xd = uf.vdat[x];
    // GData &gd = uf.gdat;

    xd.esum += w;
  }
};
// https://github.com/miscalculation53/library/tree/wip/ds/coordinate_compression.hpp

template <class T>
struct CoordinateCompression
{
  vc<T> vals;
  CoordinateCompression(const vc<T> &vec) : vals(sortuniqued(vec)) {}

  T get_val(const int i) const
  {
    assert(0 <= i && i < SZ(vals));
    return vals[i];
  }
  
  template <class I = ll>
  I get_id(const T &val) const
  {
    auto it = lower_bound(ALL(vals), val);
    if (it == vals.end() || *it != val)
      return -1;
    return it - vals.begin();
  }

  template <class I = ll>
  I size() const { return vals.size(); }
};

// https://github.com/miscalculation53/library/tree/wip/ds/meldable_set_pool.hpp

struct MeldableSetPool
{
  using Root = int;
  static constexpr Root null = -1;

private:
  struct Node
  {
    ll count;
    union
    {
      ull bits;
      array<Root, 2> child;
    };
    explicit Node(ull bits) : count(__builtin_popcountll(bits)), bits(bits) {}
    Node(Root left, Root right, ll count) : count(count), child{left, right} {}
  };

  ll n = 0;
  int height = 0;
  vc<Node> nodes;

  static ull low_mask(int k) { return k == 64 ? ~0ULL : (1ULL << k) - 1; }
  ll count_of(Root root) const { return root == null ? 0 : nodes[root].count; }
  void check_root(Root root) const
  {
    assert(root == null || (0 <= root && root < SZ<int>(nodes)));
  }
  void pull(Root root)
  {
    nodes[root].count = count_of(nodes[root].child[0]) + count_of(nodes[root].child[1]);
  }

  Root make_path(ull key, int h)
  {
    Root root = nodes.size();
    nodes.eb(1ULL << (key & 63));
    key >>= 6;
    repi(i, h)
    {
      Root parent = nodes.size();
      if ((key >> i) & 1) nodes.eb(null, root, 1);
      else nodes.eb(root, null, 1);
      root = parent;
    }
    return root;
  }

  Root insert_impl(Root root, ull key, int h, bool &inserted)
  {
    if (root == null)
    {
      inserted = true;
      return make_path(key, h);
    }
    if (h == 0)
    {
      ull bit = 1ULL << (key & 63);
      inserted = !(nodes[root].bits & bit);
      nodes[root].bits |= bit;
      nodes[root].count += inserted;
      return root;
    }
    int b = (key >> (h + 5)) & 1;
    Root child = insert_impl(nodes[root].child[b], key, h - 1, inserted);
    nodes[root].child[b] = child;
    pull(root);
    return root;
  }

  Root erase_impl(Root root, ull key, int h, bool &erased)
  {
    if (root == null) return null;
    if (h == 0)
    {
      ull bit = 1ULL << (key & 63);
      erased = (nodes[root].bits & bit) != 0;
      nodes[root].bits &= ~bit;
      nodes[root].count -= erased;
    }
    else
    {
      int b = (key >> (h + 5)) & 1;
      nodes[root].child[b] = erase_impl(nodes[root].child[b], key, h - 1, erased);
      pull(root);
    }
    return nodes[root].count == 0 ? null : root;
  }

  Root merge_impl(Root a, Root b, int h)
  {
    if (a == null) return b;
    if (b == null) return a;
    if (h == 0)
    {
      nodes[a].bits |= nodes[b].bits;
      nodes[a].count = __builtin_popcountll(nodes[a].bits);
    }
    else
    {
      nodes[a].child[0] = merge_impl(nodes[a].child[0], nodes[b].child[0], h - 1);
      nodes[a].child[1] = merge_impl(nodes[a].child[1], nodes[b].child[1], h - 1);
      pull(a);
    }
    return a;
  }

  Root clone_impl(Root root, int h)
  {
    if (root == null) return null;
    Node node = nodes[root];
    Root res = nodes.size();
    nodes.eb(node);
    if (h > 0)
    {
      Root left = clone_impl(node.child[0], h - 1);
      Root right = clone_impl(node.child[1], h - 1);
      nodes[res].child = {left, right};
    }
    return res;
  }

public:
  explicit MeldableSetPool(ll n = 0) : n(n)
  {
    assert(n >= 0);
    ull blocks = (ull(n) + 63) / 64;
    while ((1ULL << height) < blocks) height++;
  }

  ll universe_size() const { return n; }
  size_t node_count() const { return nodes.size(); }
  void reserve(size_t count) { nodes.reserve(count); }

  ll size(Root root) const { check_root(root); return count_of(root); }
  ll count(Root root) const { return size(root); }
  bool empty(Root root) const { check_root(root); return root == null; }

  Root make_empty() const { return null; }

  Root singleton(ll key)
  {
    assert(0 <= key && key < n);
    return make_path(ull(key), height);
  }

  bool contains(Root root, ll key) const
  {
    check_root(root);
    assert(0 <= key && key < n);
    for (int h = height; h > 0 && root != null; h--)
      root = nodes[root].child[(ull(key) >> (h + 5)) & 1];
    return root != null && ((nodes[root].bits >> (key & 63)) & 1);
  }

  bool insert(Root &root, ll key)
  {
    check_root(root);
    assert(0 <= key && key < n);
    bool inserted = false;
    root = insert_impl(root, ull(key), height, inserted);
    return inserted;
  }

  bool erase(Root &root, ll key)
  {
    check_root(root);
    assert(0 <= key && key < n);
    bool erased = false;
    root = erase_impl(root, ull(key), height, erased);
    return erased;
  }

  Root merge(Root &a, Root &b)
  {
    check_root(a), check_root(b);
    if (&a == &b) return a;
    assert(a == null || b == null || a != b);
    a = merge_impl(a, b, height);
    b = null;
    return a;
  }

  Root clone(Root root) { check_root(root); return clone_impl(root, height); }

  ll lt_cnt(Root root, ll key) const
  {
    check_root(root);
    if (key <= 0) return 0;
    if (key >= n) return count_of(root);
    ll res = 0;
    for (int h = height; h > 0 && root != null; h--)
    {
      int b = (ull(key) >> (h + 5)) & 1;
      if (b) res += count_of(nodes[root].child[0]);
      root = nodes[root].child[b];
    }
    if (root != null) res += __builtin_popcountll(nodes[root].bits & low_mask(key & 63));
    return res;
  }
  ll leq_cnt(Root root, ll key) const { return key >= n - 1 ? size(root) : lt_cnt(root, key + 1); }
  ll geq_cnt(Root root, ll key) const { return size(root) - lt_cnt(root, key); }
  ll gt_cnt(Root root, ll key) const { return size(root) - leq_cnt(root, key); }

  ll count(Root root, ll l, ll r) const
  {
    assert(0 <= l && l <= r && r <= n);
    return lt_cnt(root, r) - lt_cnt(root, l);
  }

  ll kth(Root root, ll k) const
  {
    check_root(root);
    assert(0 <= k && k < count_of(root));
    ull block = 0;
    for (int h = height; h > 0; h--)
    {
      ll left = count_of(nodes[root].child[0]);
      int b = k >= left;
      if (b) k -= left;
      root = nodes[root].child[b];
      block = (block << 1) | b;
    }
    ull bits = nodes[root].bits;
    int offset = 0;
    for (int step = 32; step > 0; step >>= 1)
    {
      int left = __builtin_popcountll(bits & low_mask(step));
      if (k >= left)
      {
        k -= left;
        bits >>= step;
        offset += step;
      }
    }
    return ll((block << 6) + offset);
  }

  ll next(Root root, ll key) const
  {
    ll k = lt_cnt(root, key);
    return k == size(root) ? n : kth(root, k);
  }
  ll prev(Root root, ll key) const
  {
    ll k = leq_cnt(root, key);
    return k == 0 ? -1 : kth(root, k - 1);
  }
  ll geq_min(Root root, ll key) const { return next(root, key); }
  ll gt_min(Root root, ll key) const { return key >= n - 1 ? n : next(root, key + 1); }
  ll leq_max(Root root, ll key) const { return prev(root, key); }
  ll lt_max(Root root, ll key) const { return key <= 0 ? -1 : prev(root, key - 1); }
  ll min_element(Root root) const { return next(root, 0); }
  ll max_element(Root root) const { return prev(root, n - 1); }

  template <class F>
  void enumerate(Root root, ll l, ll r, const F &f) const;

  vc<ll> content(Root root) const
  {
    vc<ll> res;
    res.reserve(size(root));
    enumerate(root, 0, n, [&](ll key) { res.eb(key); });
    return res;
  }

  class const_iterator
  {
    friend struct MeldableSetPool;
    const MeldableSetPool *sets = nullptr;
    Root root = null;
    ll key = 0;
    const_iterator(const MeldableSetPool *sets, Root root, ll key) : sets(sets), root(root), key(key) {}

  public:
    using iterator_category = input_iterator_tag;
    using value_type = ll;
    using difference_type = ptrdiff_t;
    using reference = ll;
    using pointer = const ll *;
    const_iterator() = default;
    ll operator*() const { return key; }
    const ll *operator->() const { return &key; }
    const_iterator &operator++() { key = sets->next(root, key + 1); return *this; }
    const_iterator operator++(int) { auto old = *this; ++*this; return old; }
    bool operator==(const const_iterator &other) const { return sets == other.sets && root == other.root && key == other.key; }
    bool operator!=(const const_iterator &other) const { return !(*this == other); }
  };
  using iterator = const_iterator;

  struct ElementRange
  {
    const MeldableSetPool *sets;
    Root root;
    iterator begin() const { return iterator(sets, root, sets->next(root, 0)); }
    iterator end() const { return iterator(sets, root, sets->n); }
  };
  ElementRange elements(Root root) const { check_root(root); return {this, root}; }

  void clear(Root &root) { check_root(root); root = null; }
  
  void clear() { nodes.clear(); }
};

vl A;
MeldableSetPool pool;

template <class EWeight_ = ll, bool need_vlist = false>
struct UFData
{
  struct VData
  {
    VData() {}

    decltype(pool.make_empty()) st;

    // 頂点 i の初期化
    VData(int i)
    {
      st = pool.singleton(A[i]);
    }
  };
  struct GData
  {

    // 頂点数 n のグラフの初期化
    GData(int)
    {

    }
  };
  using EWeight = EWeight_;
  template <class UF>
  static void add_edge_diff(UF &uf, int x, int y, EWeight)
  {
    VData &xd = uf.vdat[x], &yd = uf.vdat[y];
    // GData &gd = uf.gdat;

    pool.merge(xd.st, yd.st);
  }
  template <class UF>
  static void add_edge_same(UF &, int, EWeight)
  {

  }
};

void main2()
{
  LL(N, M, Q);
  VEC(ll, N, A_);
  A = A_;
  VEC(tlll, M, UVW);
  offset(UVW, tlll{-1, -1, 0});
  UNZIP(UVW, U, V, W);
  CoordinateCompression cc(W);
  vvc<pll> uvs(M + 1);
  fec([ u, v, w ] : UVW) uvs[cc.get_id(w)].eb(u, v);
  VEC(pll, Q, SC);
  offset(SC, pll{-1, 0});
  pool = (decltype(pool))(N + 1);

  UnionFind<UFData<>> uf(N);
  vvl qs(M + 1);
  auto judge = [&](const vl &D)
  {
    pool.clear();
    uf = (decltype(uf))(N);
    fem(qsi : qs) qsi.clear();
    vb res(Q);
    rep(q, Q)
    {
      if (D[q] == M + 1)
        res[q] = true;
      else if (D[q] == -1)
        res[q] = false;
      else 
        qs[D[q]].eb(q);
    }
    dump(D | cp::index(), uvs | cp::index(), qs | cp::index());
    rep(j, M + 1)
    {
      fe(q : qs[j])
      {
        auto [s, c] = SC[q];
        res[q] = (int)pool.size(uf.get_vdata(s).st) >= c;
      }
      fec([ u, v ] : uvs[j]) uf.merge(u, v);
    }
    dump(res | cp::index());
    return res;
  };
  auto ans = parallel_binsearch(Q, judge, M + 1, -1).first;
  dump(ans | cp::index());
  fem(ansi : ans)
  {
    if (ansi == M + 1)
      ansi = -1;
    else if (ansi == 0)
      ansi = 0;
    else 
      ansi = cc.get_val(ansi - 1);
  }
  PRINTV(ans);
}

void test()
{

}

// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp

template <auto init, auto main2, auto test>
struct Main
{
  Main()
  {
    cauto CERR = [](string val, string color)
    {
      string s = "\033[" + color + "m" + val + "\033[m";
      
    };
  
    CERR("\n[FAST_IO]\n\n", "32");
    
    cout << fixed << setprecision(20);
  
    init();
    
    CERR("\n[SINGLE_TESTCASE]\n\n", "36");
    main2();
  }
};
Main<init, main2, test> main_dummy;
int main() {}