MKnez's ConstructiveForces Task

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \leq t \leq 100$$$). The description of the test cases follows.

The only line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 1000$$$) — the length of the array.

Output:

For each test case, print "YES" if an array of length $$$n$$$ satisfying the conditions exists. Otherwise, print "NO". If the answer is "YES", on the next line print a sequence $$$s_1,s_2, \ldots, s_n$$$ satisfying the conditions. Each element should be a non-zero integer in the range $$$[-5000,5000]$$$, i. e. $$$-5000 \leq s_i \leq 5000$$$ and $$$s_i \neq 0$$$ should hold for each $$$1 \leq i \leq n$$$.

It can be proved that if a solution exists then there also exists one which satisfies the additional constraints on the range.

If there are several correct answers, print any of them.

Sample Input:

2
2
3

Sample Output:

YES
9 5
NO

Note:

In the first test case, $$$[9,5]$$$ is a valid answer since $$$9+5$$$ (the sum of the two adjacent elements $$$s_1+s_2$$$) is equal to $$$9+5$$$ (the sum of all elements). Other solutions include $$$[6,-9], [-1,-2], [-5000,5000], \ldots$$$

For the second test case, let us show why some arrays do not satisfy the constraints:

• $$$[1,1,1]$$$  — $$$s_1+s_2 = 1+1 = 2$$$ and $$$s_1+s_2+s_3=1+1+1 = 3$$$ differ;
• $$$[1,-1,1]$$$  — $$$s_1+s_2=1+(-1)=0$$$ and $$$s_1+s_2+s_3=1+(-1)+1 = 1$$$ differ;
• $$$[0,0,0]$$$  — The array $$$s$$$ cannot contain a $$$0$$$.

This is not a proof, but it can be shown that the answer is "NO".