#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
vc<T> concat(vc<T> &first, const Vectors &... others) {
  vc<T> res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
  return res;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
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, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

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

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

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) \
  SHOW_IMPL(__VA_ARGS__, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
  print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"

#line 2 "/home/maspy/compro/library/ds/fastset.hpp"

// 64-ary tree
// space: (N/63) * u64
struct FastSet {
  static constexpr u32 B = 64;
  int n, log;
  vvc<u64> seg;

  FastSet() {}
  FastSet(int n) { build(n); }

  int size() { return n; }

  template <typename F>
  FastSet(int n, F f) {
    build(n, f);
  }

  void build(int m) {
    seg.clear();
    n = m;
    do {
      seg.push_back(vc<u64>((m + B - 1) / B));
      m = (m + B - 1) / B;
    } while (m > 1);
    log = len(seg);
  }
  template <typename F>
  void build(int n, F f) {
    build(n);
    FOR(i, n) { seg[0][i / B] |= u64(f(i)) << (i % B); }
    FOR(h, log - 1) {
      FOR(i, len(seg[h])) {
        seg[h + 1][i / B] |= u64(bool(seg[h][i])) << (i % B);
      }
    }
  }

  bool operator[](int i) const { return seg[0][i / B] >> (i % B) & 1; }
  void insert(int i) {
    for (int h = 0; h < log; h++) {
      seg[h][i / B] |= u64(1) << (i % B), i /= B;
    }
  }
  void add(int i) { insert(i); }
  void erase(int i) {
    u64 x = 0;
    for (int h = 0; h < log; h++) {
      seg[h][i / B] &= ~(u64(1) << (i % B));
      seg[h][i / B] |= x << (i % B);
      x = bool(seg[h][i / B]);
      i /= B;
    }
  }
  void remove(int i) { erase(i); }

  // min[x,n) or n
  int next(int i) {
    assert(i <= n);
    chmax(i, 0);
    for (int h = 0; h < log; h++) {
      if (i / B == seg[h].size()) break;
      u64 d = seg[h][i / B] >> (i % B);
      if (!d) {
        i = i / B + 1;
        continue;
      }
      i += lowbit(d);
      for (int g = h - 1; g >= 0; g--) {
        i *= B;
        i += lowbit(seg[g][i / B]);
      }
      return i;
    }
    return n;
  }

  // max [0,x], or -1
  int prev(int i) {
    assert(i >= -1);
    if (i >= n) i = n - 1;
    for (int h = 0; h < log; h++) {
      if (i == -1) break;
      u64 d = seg[h][i / B] << (63 - i % B);
      if (!d) {
        i = i / B - 1;
        continue;
      }
      i -= __builtin_clzll(d);
      for (int g = h - 1; g >= 0; g--) {
        i *= B;
        i += topbit(seg[g][i / B]);
      }
      return i;
    }
    return -1;
  }

  bool any(int l, int r) { return next(l) < r; }

  // [l, r)
  template <typename F>
  void enumerate(int l, int r, F f) {
    for (int x = next(l); x < r; x = next(x + 1)) f(x);
  }

  string to_string() {
    string s(n, '?');
    for (int i = 0; i < n; ++i) s[i] = ((*this)[i] ? '1' : '0');
    return s;
  }
};
#line 2 "/home/maspy/compro/library/ds/sortable_array.hpp"

// int 列を扱う. key の重複可.
template <int NODES>
struct Sortable_Array {
  const int N, KEY_MAX;

  struct Node {
    int size;
    Node *l, *r;
  };
  Node* pool;
  int pid;
  using np = Node*;

  FastSet ss;      // 区間の左端全体を表す fastset
  vector<np> root; // 区間の左端に、dynamic segtree の node を乗せる
  vector<bool> rev;

  Sortable_Array(int KEY_MAX, vector<int> key)
      : N(key.size()), KEY_MAX(KEY_MAX), pid(0), ss(key.size()) {
    pool = new Node[NODES];
    init(key);
  }

  void set(int i, int key) {
    assert(0 <= key && key < KEY_MAX);
    split_at(i), split_at(i + 1);
    rev[i] = 0, root[i] = new_node(0);
    set_rec(root[i], 0, KEY_MAX, key);
  }

  void sort_inc(int l, int r) {
    if (l == r) return;
    split_at(l), split_at(r);
    while (1) {
      if (pid > NODES * 0.9) rebuild();
      np c = root[l];
      int i = ss.next(l + 1);
      if (i == r) break;
      root[l] = merge(0, KEY_MAX, c, root[i]);
      ss.erase(i);
    }
    rev[l] = 0;
  };

  void sort_dec(int l, int r) {
    if (l == r) return;
    if (pid > NODES * 0.9) rebuild();
    sort_inc(l, r), rev[l] = 1;
  };

  vc<int> get_all() {
    vector<int> key;
    key.reserve(N);
    auto dfs = [&](auto& dfs, np n, int l, int r, bool rev) -> void {
      if (!n || !n->size) return;
      if (r == l + 1) {
        FOR(n->size) key.eb(l);
        return;
      }
      int m = (l + r) / 2;
      if (!rev) { dfs(dfs, n->l, l, m, rev), dfs(dfs, n->r, m, r, rev); }
      if (rev) { dfs(dfs, n->r, m, r, rev), dfs(dfs, n->l, l, m, rev); }
    };
    for (int i = 0; i < N; ++i) {
      if (ss[i]) dfs(dfs, root[i], 0, KEY_MAX, rev[i]);
    }
    return key;
  }

  int get(int idx) {
    auto dfs = [&](auto& dfs, np n, int l, int r, int k) -> int {
      if (r == l + 1) { return l; }
      int m = (l + r) / 2;
      int s = (n->l ? n->l->size : 0);
      if (k < s) return dfs(dfs, n->l, l, m, k);
      return dfs(dfs, n->r, m, r, k - s);
    };
    int i = ss.prev(idx);
    int k = idx - i;
    int s = root[i]->size;
    if (rev[i]) k = s - 1 - k;
    return dfs(dfs, root[i], 0, KEY_MAX, k);
  }

private:
  void init(vector<int>& key) {
    rev.assign(N, 0), root.clear(), root.reserve(N);
    ss.build(N, [&](int i) -> int { return 1; });
    for (int i = 0; i < N; ++i) {
      root.eb(new_node(0));
      assert(key[i] < KEY_MAX);
      set_rec(root[i], 0, KEY_MAX, key[i]);
    }
  }

  // x が左端になるようにする
  void split_at(int x) {
    if (x == N || ss[x]) return;
    int a = ss.prev(x), b = ss.next(a + 1);
    ss.insert(x);
    if (!rev[a]) {
      auto [nl, nr] = split(root[a], 0, KEY_MAX, x - a);
      root[a] = nl, root[x] = nr;
      rev[a] = rev[x] = 0;
    } else {
      auto [nl, nr] = split(root[a], 0, KEY_MAX, b - x);
      root[a] = nr, root[x] = nl;
      rev[a] = rev[x] = 1;
    }
  }

  void rebuild() {
    auto key = get_all();
    pid = 0;
    init(key);
  }

  np new_node(int size) {
    assert(pid < NODES);
    pool[pid].l = pool[pid].r = nullptr;
    pool[pid].size = size;
    return &(pool[pid++]);
  }

  pair<np, np> split(np n, int l, int r, int k) {
    if (k == 0) { return {nullptr, n}; }
    if (k == n->size) { return {n, nullptr}; }
    if (r == l + 1) {
      int s = n->size;
      n->size = k;
      Node* b = new_node(s - k);
      return {n, b};
    }
    int s = (n->l ? n->l->size : 0);
    Node* b = new_node(0);
    int m = (l + r) / 2;
    if (k <= s) {
      auto [nl, nr] = split(n->l, l, m, k);
      b->l = nr, b->r = n->r, n->l = nl, n->r = nullptr;
    }
    if (k > s) {
      auto [nl, nr] = split(n->r, m, r, k - s);
      n->l = n->l, n->r = nl, b->l = nullptr, b->r = nr;
    }
    update(n), update(b);
    return {n, b};
  }

  np merge(int l, int r, np a, np b) {
    if (!a) return b;
    if (!b) return a;
    if (r == l + 1) {
      a->size += b->size;
      return a;
    }
    int m = (l + r) / 2;
    a->l = merge(l, m, a->l, b->l), a->r = merge(m, r, a->r, b->r);
    update(a);
    return a;
  }

  void update(np n) {
    if (!(n->l) && !(n->r)) { return; }
    if (!(n->l)) {
      n->size = n->r->size;
      return;
    }
    if (!(n->r)) {
      n->size = n->l->size;
      return;
    }
    n->size = n->l->size + n->r->size;
  }

  void set_rec(np n, int l, int r, int k) {
    if (r == l + 1) {
      n->size = 1;
      return;
    }
    int m = (l + r) / 2;
    if (k < m) {
      if (!(n->l)) n->l = new_node(0);
      set_rec(n->l, l, m, k);
    }
    if (m <= k) {
      if (!(n->r)) n->r = new_node(0);
      set_rec(n->r, m, r, k);
    }
    update(n);
  }
};
#line 5 "main.cpp"

void solve() {
  LL(N, Q);
  VEC(ll, A, N);
  vc<tuple<ll, ll, ll>> query;
  vi X = A;
  FOR(Q) {
    INT(t);
    if (t == 1) {
      LL(k, x);
      query.eb(t, --k, x);
      X.eb(x);
    }
    if (t == 2) { query.eb(t, -1, -1); }
    if (t == 3) {
      LL(k);
      query.eb(t, --k, -1);
    }
  }
  UNIQUE(X);
  for (auto& x: A) x = LB(X, x);

  vc<int> now(N);
  FOR(i, N) now[i] = A[i];
  Sortable_Array<20000000> SA(len(X), now);

  for (auto& [t, k, x]: query) {
    if (t == 1) {
      x = LB(X, x);
      SA.set(k, x);
    }
    if (t == 2) { SA.sort_inc(0, N); }
    if (t == 3) {
      ll x = SA.get(k);
      print(X[x]);
    }
  }
}

signed main() {
  int T = 1;
  // INT(T);
  FOR(T) solve();
  return 0;
}