Communist Revolution Game

There are $n$ people in a group, numbered from $1$ to $n$. Initially, person $i$ has exactly $i$ coins.

You can perform a revolution as follows:

• Select a person remaining in the group, and confiscate all of their coins.
• Remove the person from the group.
• Share the confiscated coins across the remaining people in the group equally into integer amounts of coins.

As explained in the third step, the revolution cannot be performed if the confiscated coins cannot be divided equally into integer amounts.

Is it possible to perform a revolution $n-1$ times in a row to make only one person remain in the end? If possible, output the sequence of persons to select at each iteration.

The first line contains the number of test cases $t$ ($t = 5$).

$t$ test cases follow starting from the next line, each consisting of a single line.

The first line of each test case contains the number of people $n$ ($1 \le n \le 100\,000$).

For each test case, output the answer as follows.

If it is possible to perform a revolution $n-1$ times in a row, output "YES" on the first line. On the next line, output $n-1$ integers $p_1,p_2,\ldots,p_{n-1}$ separated by spaces. Here, is the number corresponding to the person removed in the -th revolution. When , the second line should be left empty because there are no revolutions performed.

This problem has $100$ input files, each generated as follows.

• Input file $1$ is exactly the example input given below.
• Input file $k$ ($2 \le k \le 100$) is generated by sampling $$ integers from the range .