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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long int getmodulo(long long int x, long long int m) {
  x %= m;
  x += m;
  x %= m;
  return x;
}
long long int getprim(long long int x) {
  long long int p = 1;
  while (x > 1) {
    x >>= 1;
    p <<= 1;
  }
  return p;
}
int getlevel(long long int x) {
  int l = 1;
  while (x > 1) {
    x >>= 1;
    l++;
    ;
  }
  return l;
}
long long int shiftval[100];
long long int shifttree[100];
int main() {
  int cases;
  scanf("%d", &cases);
  for (int cas = 0; cas < cases; cas++) {
    int t;
    scanf("%d", &t);
    if (t == 1) {
      long long int x, k;
      scanf("%I64d %I64d", &x, &k);
      long long int p = getprim(x);
      long long int l = getlevel(x);
      shiftval[l] = getmodulo(shiftval[l] + k, p);
    } else if (t == 2) {
      long long int x, k;
      scanf("%I64d %I64d", &x, &k);
      long long int p = getprim(x);
      long long int l = getlevel(x);
      shifttree[l] = getmodulo(shifttree[l] + k, p);
    } else {
      long long int val;
      scanf("%I64d", &val);
      printf("%I64d", val);
      while (val > 1) {
        long long int p = getprim(val);
        long long int l = getlevel(val);
        long long int pos =
            getmodulo(val - p + shifttree[l] + shiftval[l], p) + p;
        pos /= 2;
        p >>= 1;
        l--;
        val = getmodulo(pos - p - shiftval[l], p) + p;
        printf(" %I64d", val);
      }
      printf("\n");
    }
  }
}