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D. Full Binary Tree Queries

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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:

- 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). - 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). - 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.

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:

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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