#4923. [Lydsy1706月赛]K小值查询 [平衡树，势能分析]

草，不会做啊不会做啊不会做啊……

题意:

维护一个长度为n的正整数序列a_1,a_2,...,a_n，支持以下两种操作：
1 k，将序列a从小到大排序，输出a_k的值。
2 k，将所有严格大于k的数a_i减去k。

sol:

平衡树，大家都会，减掉 \(k\) 后，相对位置发生改变的，只有 \([1,k]\) 和 \([k+1,2k]\)。
我们发现这个减法，如果减成功了，不会超过 \(\log\) 次的。

所以复杂度是 \(n \log^2 n\)，大概是和启发式合并一样>_<。

具体点的做法大概就是，你根据值域分成三个部分，[1,k] && [k+1,2k] && [2k+1,inf]。
然后我们只需要将 \([1,k]\) 和 \([k+1,2k]\) 有序的合并就好了。
怎么合并呢？你发现\([k+1,2k]\)的权值的相对大小还是不变的，那么我们就直接递归把一个个点提取出来然后合并qwq。

  int Merge(int x, int y) {
    if (sz[x] < sz[y]) x ^= y ^= x ^= y;
    if (!y) return x;
    pushdown(x);
    pushdown(y);
    x = Merge(x, merge(ls[y], rs[y]));
    ls[y] = rs[y] = 0;
    sz[y] = 1;
    int qwq1, qwq2;
    split(x, qwq1, qwq2, val[y]);
    return x = merge(merge(qwq1, y), qwq2);
  }

// powered by c++11
// by Isaunoya
#pragma GCC optimize(3)
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>

#define rep(i, x, y) for (register int i = (x); i <= (y); ++i)
#define Rep(i, x, y) for (register int i = (x); i >= (y); --i)

using namespace std;
using db = double;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;

using pii = pair<int, int>;

#define fir first
#define sec second

template <class T>

void cmax(T& x, const T& y) {
  if (x < y) x = y;
}

template <class T>

void cmin(T& x, const T& y) {
  if (x > y) x = y;
}

#define all(v) v.begin(), v.end()
#define sz(v) ((int)v.size())
#define pb emplace_back

template <class T>

void sort(vector<T>& v) {
  sort(all(v));
}

template <class T>

void reverse(vector<T>& v) {
  reverse(all(v));
}

template <class T>

void unique(vector<T>& v) {
  sort(all(v)), v.erase(unique(all(v)), v.end());
}

void reverse(string& s) { reverse(s.begin(), s.end()); }

const int io_size = 1 << 23 | 233;
const int io_limit = 1 << 22;
struct io_in {
  char ch;
#ifndef __WIN64
  char getchar() {
    static char buf[io_size], *p1 = buf, *p2 = buf;

    return (p1 == p2) && (p2 = (p1 = buf) + fread(buf, 1, io_size, stdin), p1 == p2) ? EOF : *p1++;
  }
#endif
  io_in& operator>>(char& c) {
    for (c = getchar(); isspace(c); c = getchar())
      ;

    return *this;
  }
  io_in& operator>>(string& s) {
    for (s.clear(); isspace(ch = getchar());)
      ;

    if (!~ch) return *this;

    for (s = ch; !isspace(ch = getchar()) && ~ch; s += ch)
      ;

    return *this;
  }

  io_in& operator>>(char* str) {
    char* cur = str;
    while (*cur) *cur++ = 0;

    for (cur = str; isspace(ch = getchar());)
      ;
    if (!~ch) return *this;

    for (*cur = ch; !isspace(ch = getchar()) && ~ch; *++cur = ch)
      ;

    return *++cur = 0, *this;
  }

  template <class T>

  void read(T& x) {
    bool f = 0;
    while ((ch = getchar()) < 48 && ~ch) f ^= (ch == 45);

    x = ~ch ? (ch ^ 48) : 0;
    while ((ch = getchar()) > 47) x = x * 10 + (ch ^ 48);
    x = f ? -x : x;
  }

  io_in& operator>>(int& x) { return read(x), *this; }

  io_in& operator>>(ll& x) { return read(x), *this; }

  io_in& operator>>(uint& x) { return read(x), *this; }

  io_in& operator>>(ull& x) { return read(x), *this; }

  io_in& operator>>(db& x) {
    read(x);
    bool f = x < 0;
    x = f ? -x : x;
    if (ch ^ '.') return *this;

    double d = 0.1;
    while ((ch = getchar()) > 47) x += d * (ch ^ 48), d *= .1;
    return x = f ? -x : x, *this;
  }
} in;

struct io_out {
  char buf[io_size], *s = buf;
  int pw[233], st[233];

  io_out() {
    set(7);
    rep(i, pw[0] = 1, 9) pw[i] = pw[i - 1] * 10;
  }

  ~io_out() { flush(); }

  void io_chk() {
    if (s - buf > io_limit) flush();
  }

  void flush() { fwrite(buf, 1, s - buf, stdout), fflush(stdout), s = buf; }

  io_out& operator<<(char c) { return *s++ = c, *this; }

  io_out& operator<<(string str) {
    for (char c : str) *s++ = c;
    return io_chk(), *this;
  }

  io_out& operator<<(char* str) {
    char* cur = str;
    while (*cur) *s++ = *cur++;
    return io_chk(), *this;
  }

  template <class T>

  void write(T x) {
    if (x < 0) *s++ = '-', x = -x;

    do {
      st[++st[0]] = x % 10, x /= 10;
    } while (x);

    while (st[0]) *s++ = st[st[0]--] ^ 48;
  }

  io_out& operator<<(int x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ll x) { return write(x), io_chk(), *this; }

  io_out& operator<<(uint x) { return write(x), io_chk(), *this; }

  io_out& operator<<(ull x) { return write(x), io_chk(), *this; }

  int len, lft, rig;

  void set(int _length) { len = _length; }

  io_out& operator<<(db x) {
    bool f = x < 0;
    x = f ? -x : x, lft = x, rig = 1. * (x - lft) * pw[len];
    return write(f ? -lft : lft), *s++ = '.', write(rig), io_chk(), *this;
  }
} out;
#define int long long

template <int sz, int mod>

struct math_t {
  math_t() {
    fac.resize(sz + 1), ifac.resize(sz + 1);
    rep(i, fac[0] = 1, sz) fac[i] = fac[i - 1] * i % mod;

    ifac[sz] = inv(fac[sz]);
    Rep(i, sz - 1, 0) ifac[i] = ifac[i + 1] * (i + 1) % mod;
  }

  vector<int> fac, ifac;

  int qpow(int x, int y) {
    int ans = 1;
    for (; y; y >>= 1, x = x * x % mod)
      if (y & 1) ans = ans * x % mod;
    return ans;
  }

  int inv(int x) { return qpow(x, mod - 2); }

  int C(int n, int m) {
    if (n < 0 || m < 0 || n < m) return 0;
    return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
  }
};

int gcd(int x, int y) { return !y ? x : gcd(y, x % y); }
int lcm(int x, int y) { return x * y / gcd(x, y); }

const int maxn = 1e5 + 51;

template <int maxn>

struct fhq {
  int rt, cnt;
  fhq() {
    rt = cnt = top = 0;
    srand(19260817);
  }
  int st[maxn], top;
  int val[maxn], ls[maxn], rs[maxn], sz[maxn], rnd[maxn];
  int tag[maxn];

  void pushtag(int x, int v) {
    tag[x] += v;
    val[x] -= v;
  }

  void pushdown(int x) {
    if (tag[x]) {
      if (ls[x]) {
        pushtag(ls[x], tag[x]);
      }
      if (rs[x]) {
        pushtag(rs[x], tag[x]);
      }
      tag[x] = 0;
    }
  }

  void pushup(int x) { sz[x] = sz[ls[x]] + sz[rs[x]] + 1; }

  int newnode(int v) {
    int now = top ? st[top--] : ++cnt;
    ls[now] = rs[now] = 0;
    val[now] = v;
    rnd[now] = rand();
    sz[now] = 1;
    return now;
  }

  int merge(int x, int y) {
    if (!x || !y) return x | y;

    pushdown(x);
    pushdown(y);

    if (rnd[x] < rnd[y]) {
      rs[x] = merge(rs[x], y);
      pushup(x);
      return x;
    } else {
      ls[y] = merge(x, ls[y]);
      pushup(y);
      return y;
    }
  }

  void split(int cur, int& x, int& y, int k) {
    if (!cur) {
      x = y = 0;
      return;
    }
    pushdown(cur);
    if (val[cur] <= k) {
      x = cur;
      split(rs[x], rs[x], y, k);
    } else {
      y = cur;
      split(ls[y], x, ls[y], k);
    }
    pushup(cur);
  }

  int qry(int x, int k) {
    pushdown(x);
    if (k <= sz[ls[x]]) {
      return qry(ls[x], k);
    }
    if (sz[ls[x]] + 1 == k) {
      return val[x];
    }
    return qry(rs[x], k - sz[ls[x]] - 1);
  }

  void ins(int v) {
    int x, y;
    split(rt, x, y, v);
    rt = merge(merge(x, newnode(v)), y);
  }

  int Merge(int x, int y) {
    if (sz[x] < sz[y]) x ^= y ^= x ^= y;
    if (!y) return x;
    pushdown(x);
    pushdown(y);
    x = Merge(x, merge(ls[y], rs[y]));
    ls[y] = rs[y] = 0;
    sz[y] = 1;
    int qwq1, qwq2;
    split(x, qwq1, qwq2, val[y]);
    return x = merge(merge(qwq1, y), qwq2);
  }
  void dec(int v) {
    int x, y, z;
    split(rt, x, y, v);
    split(y, y, z, v * 2);
    pushtag(y, v);
    pushtag(z, v);
    rt = merge(Merge(x, y), z);
  }
};

fhq<maxn> qwq;

signed main() {
  // code begin.
  int _, __;
  in >> _ >> __;
  while (_--) {
    int ___;
    in >> ___;
    qwq.ins(___);
  }
  while (__--) {
    int op, k;
    in >> op >> k;
    if (op == 1) {
      out << qwq.qry(qwq.rt, k) << '\n';
    } else {
      qwq.dec(k);
    }
  }
  return 0;
  // code end.
}