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:
import sys
range = xrange
input = raw_input

out = []

maxlevel = 61
shifts = [0]*maxlevel
mods = [1] + [2**(i-1) for i in range(1,maxlevel)]
q = int(input())
inp = [int(x) for line in sys.stdin for x in line.split()]
ii = 0
for _ in range(q):
    T = inp[ii]
    ii+=1
    if T==1:
        X = inp[ii]
        ii+=1
        
        level = 0
        while X>0:
            X//=2
            level+=1

        K = inp[ii]%mods[level]
        ii+=1
        shifts[level]+=K
        shifts[level]%=mods[level]

    elif T==2:
        X = inp[ii]
        ii+=1

        level = 0
        while X>0:
            X//=2
            level+=1
        
        K = inp[ii]%mods[level]
        ii+=1
         
        for i in range(level,maxlevel):
            shifts[i]+=K
            shifts[i]%=mods[i]
            if i+1<maxlevel:
                K*=2
    else:
        X = inp[ii]
        ii+=1
        Y = X
        level = 0
        while Y>0:
            Y//=2
            level+=1

        basic = mods[level]
        shift = -shifts[level]
        X = basic+((-shift+X-basic)%basic)

        nodes = []
        while X>0:
            nodes.append(X)
            X//=2
        #print(nodes)
        #print(shifts)
        #print(mods)
        outs = []
        for i in range(level):
            basic = mods[level-i]
            shift = shifts[level-i]
            node = nodes[i]
            outs.append(basic+((-shift+node-basic)%basic))
        
        print ' '.join([str(AB) for AB in outs])