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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int q;
  cin >> q;
  long long s1[60] = {};
  long long s2[60] = {};
  for (int i = 0; i < q; ++i) {
    int t;
    cin >> t;
    long long x;
    cin >> x;
    int level = log2(x);
    long long m = 1LL << level;
    if (t == 3) {
      long long pos = x - m;
      long long shift = s1[level];
      for (int i = 0; i <= level; ++i) {
        shift += s2[i] * (1LL << (level - i));
      }
      shift %= m;
      pos = (pos + shift) % m;
      cout << fixed << x << " ";
      for (int i = level - 1; i >= 0; --i) {
        pos /= 2;
        m >>= 1;
        shift = s1[i];
        for (int j = 0; j <= i; ++j) {
          shift += s2[j] * (1LL << (i - j));
        }
        shift %= m;
        long long val = (pos - shift + m) % m + m;
        cout << fixed << val << " ";
      }
      cout << endl;
    } else {
      long long k;
      cin >> k;
      if (t == 1) {
        s1[level] = (((s1[level] + k) % m) + m) % m;
      } else {
        s2[level] = (((s2[level] + k) % m) + m) % m;
      }
    }
  }
  return 0;
}