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:
import java.io.*;
import java.util.*;
import java.math.*;

public class D {
	public static void main(String[] args) throws IOException {

		/**/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		/*/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(new FileInputStream("src/d.in"))));
		/**/
		
		long[] cores = new long[63];
		TreeMap<Long, Integer> revcores = new TreeMap<>();
		for (int i = 0; i < 63; i++) {
			cores[i] = 1l<<i;
			revcores.put(1l<<i, i);
		}
		long safeAdd = 1l<<62;
		
		long[] shifts = new long[63];
		
		int q = sc.nextInt();
		for (int i = 0; i < q; i++) {
			int t = sc.nextInt();
			if (t==1||t==2) {
				long x = sc.nextLong();
				long k = sc.nextLong();
				int level = revcores.floorEntry(x).getValue();
				shifts[level] += k+safeAdd;
				shifts[level] %= cores[level];
				if (t==1) {
					shifts[level+1] -= 2*k-safeAdd;
					shifts[level+1] %= cores[level+1];
				}
			} else {
				StringBuilder ans = new StringBuilder();
				long x = sc.nextLong();
				ans.append(x);
				int level = revcores.floorEntry(x).getValue();
				while (x > 1) {
					x += shifts[level];
					x %= cores[level];
					x += cores[level];
					x/=2;
					--level;
					ans.append(" ");
					ans.append(x);
				}
				System.out.println(ans);
			}
		}
	}
}