Problem: One day two students, Grisha and Diana, found themselves in the university chemistry lab. In the lab the students found n test tubes with mercury numbered from 1 to n and decided to conduct an experiment.

The experiment consists of q steps. On each step, one of the following actions occurs:

  1. Diana pours all the contents from tube number pi and then pours there exactly xi liters of mercury. 
  2. Let's consider all the ways to add vi liters of water into the tubes; for each way let's count the volume of liquid (water and mercury) in the tube with water with maximum amount of liquid; finally let's find the minimum among counted maximums. That is the number the students want to count. At that, the students don't actually pour the mercury. They perform calculations without changing the contents of the tubes. 



Unfortunately, the calculations proved to be too complex and the students asked you to help them. Help them conduct the described experiment.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 105) — the number of tubes ans the number of experiment steps. The next line contains n space-separated integers: h1, h2, ..., hn (0 ≤ hi ≤ 109), where hi is the volume of mercury in the і-th tube at the beginning of the experiment.

The next q lines contain the game actions in the following format:

  * A line of form "1 pi xi" means an action of the first type (1 ≤ pi ≤ n; 0 ≤ xi ≤ 109). 
  * A line of form "2 vi" means an action of the second type (1 ≤ vi ≤ 1015). 



It is guaranteed that there is at least one action of the second type. It is guaranteed that all numbers that describe the experiment are integers.

Output

For each action of the second type print the calculated value. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.

Examples

Input

3 3
1 2 0
2 2
1 2 1
2 3


Output

1.50000
1.66667


Input

4 5
1 3 0 1
2 3
2 1
1 3 2
2 3
2 4


Output

1.66667
1.00000
2.33333
2.66667

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << '{';
  string sep;
  for (const auto &x : v) os << sep << x, sep = ", ";
  return os << '}';
}
template <typename T, size_t size>
ostream &operator<<(ostream &os, const array<T, size> &arr) {
  os << '{';
  string sep;
  for (const auto &x : arr) os << sep << x, sep = ", ";
  return os << '}';
}
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p) {
  return os << '(' << p.first << ", " << p.second << ')';
}
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cerr << ' ' << H;
  dbg_out(T...);
}
using splay_key = int;
struct splay_node {
  splay_node *parent = nullptr, *child[2] = {nullptr, nullptr};
  splay_key key;
  int size = 1;
  int64_t sum = 0;
  static int get_size(splay_node *x) { return x == nullptr ? 0 : x->size; }
  static int64_t get_sum(splay_node *x) { return x == nullptr ? 0 : x->sum; }
  int parent_index() const {
    if (parent == nullptr) return -1;
    return this == parent->child[0] ? 0 : 1;
  }
  void set_child(int index, splay_node *x) {
    child[index] = x;
    if (x != nullptr) x->parent = this;
  }
  void join() {
    size = get_size(child[0]) + get_size(child[1]) + 1;
    sum = get_sum(child[0]) + get_sum(child[1]) + key;
  }
};
auto random_address = [] {
  char *p = new char;
  delete p;
  return uint64_t(p);
};
mt19937_64 splay_rng(chrono::steady_clock::now().time_since_epoch().count() *
                     (random_address() | 1));
int64_t splay_count = 0;
struct splay_tree {
  static const int POOL_SIZE = 10000;
  static vector<splay_node *> node_pool;
  static vector<splay_node *> pointers_to_delete;
  static splay_node *new_node(const splay_key &key) {
    if (node_pool.empty()) {
      splay_node *ptr = new splay_node[POOL_SIZE];
      pointers_to_delete.push_back(ptr);
      for (int i = POOL_SIZE - 1; i >= 0; i--) node_pool.push_back(ptr + i);
    }
    splay_node *node = node_pool.back();
    node_pool.pop_back();
    node->key = key;
    node->join();
    return node;
  }
  static bool _exit_delete_setup;
  static void _delete_pointers() {
    for (splay_node *node : pointers_to_delete) delete[] node;
    pointers_to_delete.clear();
  }
  ~splay_tree() {
    if (!_exit_delete_setup) {
      atexit(_delete_pointers);
      _exit_delete_setup = true;
    }
  }
  splay_node *root = nullptr;
  bool empty() const { return root == nullptr; }
  int size() const { return root == nullptr ? 0 : root->size; }
  splay_node *set_root(splay_node *x) {
    if (x != nullptr) x->parent = nullptr;
    return root = x;
  }
  void rotate_up(splay_node *x, bool x_join = true) {
    splay_node *p = x->parent, *gp = p->parent;
    int index = x->parent_index();
    if (gp == nullptr)
      set_root(x);
    else
      gp->set_child(p->parent_index(), x);
    p->set_child(index, x->child[!index]);
    x->set_child(!index, p);
    p->join();
    if (x_join) x->join();
  }
  void splay(splay_node *x) {
    splay_count++;
    while (x != root) {
      splay_node *p = x->parent;
      if (p != root)
        rotate_up(x->parent_index() == p->parent_index() ? p : x, false);
      rotate_up(x, false);
    }
    x->join();
  }
  static constexpr double SPLAY_RNG_RANGE = double(splay_rng.max()) + 1.0;
  static constexpr double LOG_CONSTANT = 2.0;
  static constexpr double SPLAY_PROBABILITY = 0.25;
  static const int SIZE_CUTOFF = 100;
  void check_splay(splay_node *x, int depth) {
    assert(x != nullptr);
    int n = size(), log_n = 32 - __builtin_clz(n);
    if (depth > LOG_CONSTANT * log_n ||
        (n < SIZE_CUTOFF &&
         double(splay_rng()) < SPLAY_PROBABILITY * SPLAY_RNG_RANGE))
      splay(x);
  }
  pair<splay_node *, int> insert(const splay_key &key,
                                 bool require_unique = false) {
    return insert(new_node(key), require_unique);
  }
  pair<splay_node *, int> insert(splay_node *x, bool require_unique = false) {
    if (root == nullptr) return {set_root(x), 0};
    splay_node *current = root, *prev = nullptr;
    int below = 0, depth = 0;
    while (current != nullptr) {
      prev = current;
      depth++;
      if (current->key < x->key) {
        below += splay_node::get_size(current->child[0]) + 1;
        current = current->child[1];
      } else {
        if (require_unique && !(x->key < current->key)) {
          below += splay_node::get_size(current->child[0]);
          check_splay(current, depth);
          return {current, below};
        }
        current = current->child[0];
      }
    }
    prev->set_child(prev->key < x->key ? 1 : 0, x);
    check_splay(x, depth);
    for (splay_node *node = x; node != nullptr; node = node->parent)
      node->join();
    return {x, below};
  }
  splay_node *begin() {
    if (root == nullptr) return nullptr;
    splay_node *x = root;
    int depth = 0;
    while (x->child[0] != nullptr) {
      x = x->child[0];
      depth++;
    }
    check_splay(x, depth);
    return x;
  }
  splay_node *successor(splay_node *x) const {
    if (x == nullptr) return nullptr;
    if (x->child[1] != nullptr) {
      x = x->child[1];
      while (x->child[0] != nullptr) x = x->child[0];
      return x;
    }
    while (x->parent_index() == 1) x = x->parent;
    return x->parent;
  }
  splay_node *predecessor(splay_node *x) const {
    if (x == nullptr) return nullptr;
    if (x->child[0] != nullptr) {
      x = x->child[0];
      while (x->child[1] != nullptr) x = x->child[1];
      return x;
    }
    while (x->parent_index() == 0) x = x->parent;
    return x->parent;
  }
  splay_node *last() {
    if (root == nullptr) return nullptr;
    splay_node *x = root;
    int depth = 0;
    while (x->child[1] != nullptr) {
      x = x->child[1];
      depth++;
    }
    check_splay(x, depth);
    return x;
  }
  void clear() {
    vector<splay_node *> nodes;
    nodes.reserve(size());
    for (splay_node *node = begin(); node != nullptr; node = successor(node))
      nodes.push_back(node);
    for (splay_node *node : nodes) {
      *node = splay_node();
      node_pool.push_back(node);
    }
    set_root(nullptr);
  }
  void erase(splay_node *x) {
    splay_node *new_x = nullptr, *fix_node = nullptr;
    if (x->child[0] == nullptr || x->child[1] == nullptr) {
      new_x = x->child[x->child[0] == nullptr ? 1 : 0];
      fix_node = x->parent;
    } else {
      splay_node *next = successor(x);
      assert(next != nullptr && next->child[0] == nullptr);
      new_x = next;
      fix_node = next->parent == x ? next : next->parent;
      next->parent->set_child(next->parent_index(), next->child[1]);
      next->set_child(0, x->child[0]);
      next->set_child(1, x->child[1]);
    }
    if (x == root)
      set_root(new_x);
    else
      x->parent->set_child(x->parent_index(), new_x);
    int depth = 0;
    for (splay_node *node = fix_node; node != nullptr; node = node->parent) {
      node->join();
      depth++;
    }
    if (fix_node != nullptr) check_splay(fix_node, depth);
    *x = splay_node();
    node_pool.push_back(x);
  }
  pair<splay_node *, int> lower_bound(const splay_key &key) {
    splay_node *current = root, *prev = nullptr, *answer = nullptr;
    int below = 0, depth = 0;
    while (current != nullptr) {
      prev = current;
      depth++;
      if (current->key < key) {
        below += splay_node::get_size(current->child[0]) + 1;
        current = current->child[1];
      } else {
        answer = current;
        current = current->child[0];
      }
    }
    if (prev != nullptr) check_splay(prev, depth);
    return make_pair(answer, below);
  }
  bool contains(const splay_key &key) {
    splay_node *node = lower_bound(key).first;
    return node != nullptr && node->key == key;
  }
  bool erase(const splay_key &key) {
    splay_node *x = lower_bound(key).first;
    if (x == nullptr || x->key != key) return false;
    erase(x);
    return true;
  }
  splay_node *node_at_index(int index) {
    if (index < 0 || index >= size()) return nullptr;
    splay_node *current = root;
    int depth = 0;
    while (current != nullptr) {
      int left_size = splay_node::get_size(current->child[0]);
      depth++;
      if (index == left_size) {
        check_splay(current, depth);
        return current;
      }
      if (index < left_size) {
        current = current->child[0];
      } else {
        current = current->child[1];
        index -= left_size + 1;
      }
    }
    assert(false);
  }
  splay_node *query_prefix_key(const splay_key &key) {
    splay_node *node = lower_bound(key).first;
    if (node == nullptr) return root;
    splay(node);
    return node->child[0];
  }
  splay_node *query_prefix_count(int count) {
    if (count <= 0) return nullptr;
    if (count >= size()) return root;
    splay_node *node = node_at_index(count);
    splay(node);
    return node->child[0];
  }
  splay_node *query_suffix_key(const splay_key &key) {
    splay_node *node = lower_bound(key).first;
    if (node == nullptr) return nullptr;
    node = predecessor(node);
    if (node == nullptr) return root;
    splay(node);
    return node->child[1];
  }
  splay_node *query_suffix_count(int count) {
    if (count >= size()) return root;
    if (count <= 0) return nullptr;
    int index = size() - count;
    splay_node *node = node_at_index(index - 1);
    splay(node);
    return node->child[1];
  }
};
bool splay_tree::_exit_delete_setup = false;
vector<splay_node *> splay_tree::node_pool;
vector<splay_node *> splay_tree::pointers_to_delete;
const int INF = 1e9 + 5;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << fixed << setprecision(8);
  int N, Q;
  cin >> N >> Q;
  splay_tree tree;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    cin >> A[i];
    tree.insert(A[i]);
  }
  for (int q = 0; q < Q; q++) {
    int type;
    cin >> type;
    if (type == 1) {
      int p, x;
      cin >> p >> x;
      p--;
      tree.erase(A[p]);
      A[p] = x;
      tree.insert(A[p]);
      continue;
    }
    int64_t v;
    cin >> v;
    auto test = [&](double ans) {
      int64_t xx = int64_t(ceil(ans));
      int x = xx > INF ? INF : int(xx);
      splay_node *node = tree.query_prefix_key(x);
      int count = splay_node::get_size(node);
      int64_t sum = splay_node::get_sum(node);
      return ans * count - sum >= v;
    };
    double low = 0, high = 1e16;
    if (test(1))
      high = 1;
    else
      low = 1;
    for (int iter = 0; iter < 60; iter++) {
      double mid = high <= 1 ? (low + high) / 2 : sqrt(low * high);
      if (test(mid))
        high = mid;
      else
        low = mid;
    }
    cout << low << '\n';
  }
}