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 $*Q*$ ($1 ≤ *Q* ≤ 10^{5}$).

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: $3$ $*X*$ ($1 ≤ *X* ≤ 10^{18}$).

Output

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

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: