CF960D.Full Binary Tree Queries

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.

The first line contains a single integer $Q$ ( $1<=Q<=10^{5}$ ).

Then $Q$ queries follow, one per line:

• Queries of type $1$ and $2$ have the following format: $T$ $X$ $K$ ( $1<=T<=2$ ; $1<=X<=10^{18}$ ; $0<=|K|<=10^{18}$ ), where $T$ is type of the query.
• Queries of type $3$ have the following format: $3$ $X$ ( $1<=X<=10^{18}$ ).

For each query of type $3$ , print the values of all nodes encountered in descending order.

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: