I. Mancala Solitaire
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

In Mancala solitaire, you are given stones in a line of holes, with hole 0 being special and containing no stones to start with.

In each turn, you choose a number $$$k$$$ such that there are exactly $$$k$$$ stones in hole $$$k$$$. Then you remove the stones from hole $$$k$$$ and put one stone each into the holes $$$k - 1, k - 2, \dots, 1, 0$$$:

The goal is to get all stones in hole 0 after some number of turns. (For example, you can do this in the above example by picking $$$k_1=3, k_2=1, k_3=2$$$, and finally $$$k_4=1$$$.)

You want to show this game to your friend and create a starting position that makes it possible for him to successfully complete the game (getting all stones in hole 0). Give such a starting position for $$$N$$$ stones. It is guaranteed that this is always possible.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \leq t \leq 100$$$), the number of test cases.

The first line of each test case contains an integer $$$N$$$ $$$(1 \leq N \leq 10^{9})$$$, the number of stones you want to place in total.

It is guaranteed that the sum of all $$$N$$$ will not exceed $$$10^9$$$.

Output

For each test case: Print one integer $$$m$$$, the number of the last hole which contains at least one stone. In the next line, print $$$m$$$ integers, the number of stones in the $$$i$$$'th hole. You can ignore hole 0.

Example
Input
3
1
4
15
Output
1
1
3
0 1 3
6
1 2 0 2 4 6