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 namespace std;
long long int Q, type, node, shifts, blue[65], green[65], lev;
vector<long long int> answer;
long long int lo, hi, mid, val, ans;
long long int nodeLevel, lowLevel, highLevel, fakeNode, realNode, realParent;
long long int level(long long int x) { return log2(x) + 1; }
long long int low(long long int l) { return exp2(l - 1); }
long long int high(long long int l) { return exp2(l) - 1; }
long long int parent(long long int x) { return (x >> 1); }
bool cmp(long long int a, long long int b) { return a > b; }
void query(long long int x) {
  nodeLevel = level(x);
  lowLevel = low(nodeLevel);
  highLevel = high(nodeLevel);
  fakeNode = (x - blue[nodeLevel] < lowLevel ? x - blue[nodeLevel] + lowLevel
                                             : x - blue[nodeLevel]);
  realParent = parent((x + green[nodeLevel] > highLevel
                           ? ((x + green[nodeLevel]) % highLevel) + lowLevel - 1
                           : x + green[nodeLevel]));
  answer.push_back(fakeNode);
  if (x == 1) return;
  query(realParent);
}
int main() {
  cin >> Q;
  for (int i = 0; i < Q; i++) {
    cin >> type;
    if (type == 1) {
      cin >> node >> shifts;
      lev = level(node);
      shifts %= low(lev);
      blue[lev] += shifts;
      if (blue[lev] > low(lev)) blue[lev] %= low(lev);
      while (blue[lev] < 0) blue[lev] += low(lev);
    } else if (type == 2) {
      cin >> node >> shifts;
      lev = level(node);
      shifts %= low(lev);
      green[lev] += shifts;
      if (green[lev] > low(lev)) green[lev] %= low(lev);
      while (green[lev] < 0) green[lev] += low(lev);
    } else if (type == 3) {
      answer.erase(answer.begin(), answer.end());
      cin >> node;
      nodeLevel = level(node);
      lowLevel = low(nodeLevel);
      highLevel = high(nodeLevel);
      realNode = (node + blue[nodeLevel] > highLevel
                      ? ((node + blue[nodeLevel]) % highLevel) + lowLevel - 1
                      : node + blue[nodeLevel]);
      query(realNode);
      sort(answer.begin(), answer.end(), cmp);
      for (auto k : answer) cout << k << " ";
      cout << "\n";
    }
  }
  return 0;
}