Problem Statement

Determine whether there is a length-$N$ sequence of positive integers $A=(A_1,A_2,\dots,A_N)$ that satisfies all of the following conditions, and if it exists, construct one.

• $\sum_{i=1}^{N} \frac{1}{A_i} = 1$
• All elements of $A$ are distinct.
• $1 \le A_i \le 10^9(1 \le i \le N)$

You are given $T$ test cases. Find the answer for each of them.

Constraints

• $1 \le T \le 500$
• $1 \le N \le 500$

Input

The input is given from Standard Input in the following format:

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Here, $\mathrm{case}_i$ is the $i$-th test case. Each test case is given in the following format:

N

Output

For each case, if there is not a sequence of positive integers $A=(A_1,A_2,\dots,A_N)$ that satisfies the conditions, print No. If there is, print one in the following format:

Yes
A_1 A_2 \dots A_N

If there are multiple valid solutions, any of them will be accepted.