D. Full Binary Tree Queries
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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:

After query 1 2 1:

After query 2 4 -1: