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 JAVA):

Solution:
//package uva;

import java.util.*;
import java.io.*;

public class Uva {
    public static long shift[] = new long[64];
    public static int getLevel(long a){
        int count = 0;
        while(a>0){
            a >>= 1;
            count++;
        }
        return count;
    }
    public static long getMinInLevel(int lvl){
        return (long)(1L<<(lvl-1));
    }
    public static long getMaxInLevel(int lvl){
        return ((long)(1L<<lvl)-1);
    }
    public static long getIndex(long X){
        int lvl = getLevel(X);
        long diff = X-getMinInLevel(lvl);
        long range = getMaxInLevel(lvl)-getMinInLevel(lvl)+1;
        long index = (diff+shift[lvl]+range)%range;
        long ans = getMinInLevel(lvl)+index;
        return index;
    }
    public static long getValue(long index,int lvl){
        long range = getMaxInLevel(lvl)-getMinInLevel(lvl)+1;
        long value = (index-shift[lvl]+range)%range;
        long ans = getMinInLevel(lvl)+value;
        return ans;
    }
    public static void main(String arg[])throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int Q = Integer.parseInt(br.readLine());
        StringTokenizer st;
        for(int i=0;i<Q;i++){
            st = new StringTokenizer(br.readLine());
            int T = Integer.parseInt(st.nextToken());
            long X = Long.parseLong(st.nextToken());
            if(T==3){
                StringBuilder sb = new StringBuilder();
                int lvl = getLevel(X);
                long index = getIndex(X);
                Queue<Long> q = new LinkedList<>();
                for(int j=lvl;j>=1;j--){
                    long value = getValue(index,j);
                    q.add(value);
                    index >>= 1;
                }
                while(!q.isEmpty()){
                    sb.append(q.poll());
                    if(q.size()>0)
                        sb.append(" ");
                }
//                sb.append('\n');
                System.out.println(sb.toString());
            }else if(T==1){
                long K = Long.parseLong(st.nextToken());
                int lvl = getLevel(X);
                long range = getMaxInLevel(lvl)-getMinInLevel(lvl)+1;
                shift[lvl] = (shift[lvl]+K+range)%range;
            }else{
                long K = Long.parseLong(st.nextToken());
                int lvl = getLevel(X);
                long range = getMaxInLevel(lvl)-getMinInLevel(lvl)+1;
                long cur = 1;
                for(int j=lvl;j<=63;j++){
                    shift[j] = (shift[j]+(((long)cur%range)*K)%range+range)%range;
                    range <<= 1;
                    cur <<= 1;
                }
            }
        }
    }
    
}