Description: Recently, your friend discovered one special operation on an integer array $$$a$$$: 1. Choose two indices $$$i$$$ and $$$j$$$ ($$$i \neq j$$$); 2. Set $$$a_i = a_j = |a_i - a_j|$$$. After playing with this operation for a while, he came to the next conclusion: - For every array $$$a$$$ of $$$n$$$ integers, where $$$1 \le a_i \le 10^9$$$, you can find a pair of indices $$$(i, j)$$$ such that the total sum of $$$a$$$ will decrease after performing the operation. This statement sounds fishy to you, so you want to find a counterexample for a given integer $$$n$$$. Can you find such counterexample and prove him wrong? In other words, find an array $$$a$$$ consisting of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) such that for all pairs of indices $$$(i, j)$$$ performing the operation won't decrease the total sum (it will increase or not change the sum). Input Format: The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. Then $$$t$$$ test cases follow. The first and only line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 1000$$$) — the length of array $$$a$$$. Output Format: For each test case, if there is no counterexample array $$$a$$$ of size $$$n$$$, print NO. Otherwise, print YES followed by the array $$$a$$$ itself ($$$1 \le a_i \le 10^9$$$). If there are multiple counterexamples, print any. Note: In the first test case, the only possible pairs of indices are $$$(1, 2)$$$ and $$$(2, 1)$$$. If you perform the operation on indices $$$(1, 2)$$$ (or $$$(2, 1)$$$), you'll get $$$a_1 = a_2 = |1 - 337| = 336$$$, or array $$$[336, 336]$$$. In both cases, the total sum increases, so this array $$$a$$$ is a counterexample.