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;
const int N = 100;
long long added[N];
long long moved[N];
long long cnt[N];
long long first_val[N];
void pre() {
  long long x = 1;
  for (int i = 1; i <= 100; i++) {
    cnt[i] = x, x *= 2;
    first_val[i] = cnt[i];
  }
}
int get_level(long long x) {
  int res = 0;
  while (x) {
    res++;
    x >>= 1;
  }
  return res;
}
long long add_mod(long long x, long long added, long long mod) {
  x -= mod;
  x += added;
  x += mod;
  x %= mod;
  x += mod;
  return x;
}
void calc(long long x, int level) {
  if (level == 1) return void(puts("1"));
  long long y = add_mod(x, -added[level], cnt[level]);
  printf("%I64d ", y);
  x = add_mod(x, moved[level], cnt[level]);
  x /= 2;
  calc(x, level - 1);
}
void fix(long long &val, long long mod) {
  if (!val) return;
  long long s = val / abs(val);
  val *= s;
  val %= mod;
  val *= s;
}
int main() {
  pre();
  int q;
  scanf("%d", &q);
  while (q--) {
    int t;
    scanf("%d", &t);
    if (t == 1 || t == 2) {
      long long x, k;
      scanf("%I64d %I64d", &x, &k);
      int level = get_level(x);
      if (t == 1)
        added[level] += k, fix(added[level], cnt[level]);
      else
        moved[level] += k, fix(moved[level], cnt[level]);
    } else {
      long long x;
      scanf("%I64d", &x);
      int level = get_level(x);
      printf("%I64d ", x);
      x = add_mod(x, added[level], cnt[level]);
      x = add_mod(x, moved[level], cnt[level]);
      if (x > 1)
        calc(x / 2, level - 1);
      else
        puts("");
    }
  }
  return 0;
}