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>
int q, t;
long long l[62], x, k;
int find(long long x) {
  int h = -1;
  while (x) x >>= 1, ++h;
  return h;
}
void shift(int lv, long long k) {
  l[lv] += k;
  l[lv] &= ((1ll << lv) - 1);
}
int main() {
  scanf("%d", &q);
  for (int i = 1; i <= q; ++i) {
    scanf("%d%lld", &t, &x);
    if (t == 1) {
      scanf("%lld", &k);
      shift(find(x), k);
    } else if (t == 2) {
      scanf("%lld", &k);
      int lv = find(x);
      for (int j = lv; j <= 61; ++j) shift(j, k << (j - lv));
    } else if (t == 3) {
      int lv = find(x);
      long long y = (x - (1ll << lv) + l[lv]) & ((1ll << lv) - 1);
      for (int j = lv; j >= 0; --j)
        printf("%lld ", ((y - l[j]) & ((1ll << j) - 1)) + (1ll << j)), y >>= 1;
      puts("");
    }
  }
}