Problem: 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: 

<image>

After query 1 2 1: 

<image>

After query 2 4 -1: 

<image>

Solution (in PYTHON):

Solution:
levels=[[0,0] for i in range(61)]
levels[0][1]=1
for i in range(1,61):
    levels[i][1]=2*levels[i-1][1]

import math
q=int(raw_input())
for e in range(q):
    s=raw_input().split()
    if(s[0]=='3'):
        x=int(s[1])
        high=int(math.log(x,2))
        pos=(x-(levels[high][1]-levels[high][0]))%levels[high][1]
        #print(levels[high])
        ans=[x,]
        for i in range(high-1,-1,-1):
            #print(x,pos,levels[i][0])
            pos//=2
            if(pos-levels[i][0]<0):
                ans.append(2*levels[i][1]-levels[i][0]+pos)
            else:
                ans.append(levels[i][1]-levels[i][0]+pos)
        for i in range(len(ans)):
            ans[i]=str(ans[i])
        s=' '.join(ans)
        print(s)
    elif(s[0]=='1'):
        x=int(s[1])
        k=int(s[2])
        high=int(math.log(x,2))
        levels[high][0]=(k+levels[high][0])%levels[high][1]
    else:
        x=int(s[1])
        k=int(s[2])
        high=int(math.log(x,2))
        for i in range(high,61):
            levels[i][0]=(k+levels[i][0])%levels[i][1]
            k*=2