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.

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:

inputFormat

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).

outputFormat

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:

样例

5
3 14
1 5 -3
3 14
1 3 1
3 14

14 7 3 1 
14 6 3 1
14 6 2 1

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