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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeSet;


/*

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

3
1 2 1
2 4 -1
3 8
 */
public class pizza {
	public static void main(String[] args) throws IOException {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int Q = in.nextInt();
		long[] nshift = new long[61];
		while(Q --> 0) {
			int type = in.nextInt();
			long x = in.nextLong();
			int level = getLevel(x);
			if(type == 1) {
				long k = in.nextLong();
				shift(nshift, level, k);
			} else if(type == 2) {
				long k = in.nextLong();
				for(int i=level;i<61;i++) {
					shift(nshift, i, k);
					k *= 2;
				}
			} else {
				long nx = shift(x,level,nshift[level]);
				while(nx > 0) {
					out.print(shift(nx,level,-nshift[level]));
					nx /= 2;
					level--;
					if(nx != 0)
						out.print(' ');
				}
				out.println();
			}
		}
		out.close();
	}
	static long shift(long node, int level, long k) {
		long m = getLevelSize(level);
		node -= m;
		node += k;
		node %= m;
		if(node < 0)
			node += m;
		node += m;
		return node;
	}
	static long first(int level) {
		return 1L << level;
	}
	static void shift(long[] arr, int level, long k) {
		long m = getLevelSize(level);
		arr[level] = (((arr[level] + k) % m) + m) % m;
	}
	static long getLevelSize(int level) {
		return 1L << level;
	}
	static int getLevel(long x) {
		if(x == 1)
			return 0;
		return getLevel(x/2)+1;
	}
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(InputStream i) {
			br = new BufferedReader(new InputStreamReader(i));
			st = null;
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
	}
}