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.

Sample Input 1

2
3
5

Sample Output 1

Yes
2 3 6 
Yes
3 4 5 6 20 

In the first test case, $N=3$.

$A=(2,3,6)$ is valid because $\\frac{1}{2} + \\frac{1}{3} + \\frac{1}{6} = 1$ and it satisfies all other conditions.

In the second test case, $N=5$.

$A=(3,4,5,6,20)$ is valid because $\\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{20} = 1$ and it satisfies all other conditions.

Note that, for example, $A=(5,5,5,5,5)$ satisfies the first and third conditions, but it is invalid because it contains duplicated elements.