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.FileNotFoundException;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Created on 5/11/2017.
 */
public class D {
    Scanner sc;
    PrintWriter pw;
    int MAX = 63;

    long[] min = new long[MAX];
    long[] max = new long[MAX];
    long[] rot = new long[MAX];
    long[] sz = new long[MAX];

    int level(long x) {
        for (int i = 0; i < MAX; i++) {
            if (min[i] <= x && x <= max[i]) {
                return i;
            }
        }

        throw new AssertionError();
    }

    void run() throws FileNotFoundException {
        // sc = new Scanner(new File("A.txt"));
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);

        min[0] = max[0] = sz[0] = 1;
        for (int i = 1; i < MAX; i++) {
            min[i] = min[i - 1] * 2;
            max[i] = max[i - 1] * 2 + 1;
            sz[i] = max[i] - min[i] + 1;
        }

        int q = sc.nextInt();

        for (int ii = 0; ii < q; ii++) {
            int t = sc.nextInt();
            if (t == 1) {
                long x = sc.nextLong();
                long k = sc.nextLong();

                int lvl = level(x);
                k %= sz[lvl];
                if (k < 0) {
                    k += sz[lvl];
                }
                rot[lvl] = (rot[lvl] + k) % sz[lvl];
            } else if (t == 2) {
                long x = sc.nextLong();
                long k = sc.nextLong();

                int lvl = level(x);
                k %= sz[lvl];
                if (k < 0) {
                    k += sz[lvl];
                }

                for (int j = lvl; j < MAX; j++) {
                    rot[j] = (rot[j] + k) % sz[j];
                    k *= 2;
                }
            } else if (t == 3) {
                long x = sc.nextLong();

                int lvl = level(x);
                long initialPos = x - min[lvl];
                long pos = (initialPos + rot[lvl]) % sz[lvl];

                pw.print(x);
                lvl--;
                for (; lvl >= 0; lvl--) {
                    pos /= 2;
                    long fromPos = (sz[lvl] + pos - rot[lvl]) % sz[lvl];
                    long val = fromPos + min[lvl];
                    // System.out.println("lvl: " + lvl + ", pos: " + pos + ", from: " + fromPos + ", val: " + val);

                    pw.print(" " + val);
                }

                pw.println();
            }
        }

        pw.close();
    }
    
    public static void main(String[] args) throws FileNotFoundException {
        D a = new D();
        a.run();
    }
}