Problem: You have a full binary tree having infinite levels.

Each node has an initial value. If a node has value x, then its left child has value 2·x and its right child has value 2·x + 1. 

The value of the root is 1. 

You need to answer Q queries. 

There are 3 types of queries: 

  1. Cyclically shift the values of all nodes on the same level as node with value X by K units. (The values/nodes of any other level are not affected).
  2. Cyclically shift the nodes on the same level as node with value X by K units. (The subtrees of these nodes will move along with them).
  3. Print the value of every node encountered on the simple path from the node with value X to the root.



Positive K implies right cyclic shift and negative K implies left cyclic shift. 

It is guaranteed that atleast one type 3 query is present.

Input

The first line contains a single integer Q (1 ≤ Q ≤ 105).

Then Q queries follow, one per line: 

  * Queries of type 1 and 2 have the following format: T X K (1 ≤ T ≤ 2; 1 ≤ X ≤ 1018; 0 ≤ |K| ≤ 1018), where T is type of the query.
  * Queries of type 3 have the following format: 3 X (1 ≤ X ≤ 1018).

Output

For each query of type 3, print the values of all nodes encountered in descending order.

Examples

Input

5
3 12
1 2 1
3 12
2 4 -1
3 8


Output

12 6 3 1 
12 6 2 1 
8 4 2 1 


Input

5
3 14
1 5 -3
3 14
1 3 1
3 14


Output

14 7 3 1 
14 6 3 1 
14 6 2 1 

Note

Following are the images of the first 4 levels of the tree in the first test case:

Original: 

<image>

After query 1 2 1: 

<image>

After query 2 4 -1: 

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using std::abs;
using std::array;
using std::cerr;
using std::cin;
using std::cout;
using std::generate;
using std::make_pair;
using std::map;
using std::max;
using std::max_element;
using std::min;
using std::min_element;
using std::pair;
using std::reverse;
using std::set;
using std::sort;
using std::string;
using std::unique;
using std::vector;
template <typename T>
T input() {
  T res;
  cin >> res;
  {};
  return res;
}
template <typename IT>
void input_seq(IT b, IT e) {
  std::generate(b, e,
                input<typename std::remove_reference<decltype(*b)>::type>);
}
int32_t main() {
  std::iostream::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  const int64_t LOG = 60;
  vector<int64_t> val_mod(LOG + 1), nod_mod(LOG + 1);
  for (int64_t q = input<int64_t>(); q != 0; --q) {
    int64_t t = input<int64_t>();
    auto get_dep = [](int64_t val) {
      int64_t ans = 0;
      while (val != 1) ans += 1, val /= 2;
      return ans;
    };
    if (t == 1) {
      int64_t dep = get_dep(input<int64_t>());
      int64_t x = input<int64_t>();
      x %= (int64_t(1) << dep);
      if (x < 0) x += (int64_t(1) << dep);
      val_mod[dep] += x;
      val_mod[dep] %= (int64_t(1) << dep);
    }
    if (t == 2) {
      int64_t dep = get_dep(input<int64_t>());
      int64_t x = input<int64_t>();
      x %= (int64_t(1) << dep);
      if (x < 0) x += (int64_t(1) << dep);
      for (int64_t i = dep; i <= LOG; ++i, x *= 2) {
        nod_mod[i] += x;
        nod_mod[i] %= (int64_t(1) << i);
      }
    }
    if (t == 3) {
      auto shift = [&](int64_t x, bool tp) {
        int64_t dep = get_dep(x);
        x -= (int64_t(1) << dep);
        x += (not tp ? nod_mod[dep] : val_mod[dep]);
        x %= (int64_t(1) << dep);
        x += (int64_t(1) << dep);
        return x;
      };
      auto shift_back = [&](int64_t x, bool tp) {
        int64_t dep = get_dep(x);
        x -= (int64_t(1) << dep);
        x -= (not tp ? nod_mod[dep] : val_mod[dep]);
        x %= (int64_t(1) << dep);
        if (x < 0) x += (int64_t(1) << dep);
        x += (int64_t(1) << dep);
        return x;
      };
      int64_t x = input<int64_t>();
      x = shift(shift(x, false), true);
      cout << shift_back(shift_back(x, true), false) << " ";
      while (x != 1) {
        x /= 2;
        cout << shift_back(shift_back(x, false), true) << " ";
      }
      cout << "\n";
    }
  }
  return 0;
}