Prove Him Wrong

题意翻译

你需要在一个整数序列 $ a $ 上执行一个操作： 1. 选择两个位置 $ i,j\;(i \ne j) $； 2. 使 $ a_i=a_j=|a_i-a_j| $。 接着有一个猜想： 对于每一个有 $ n $ 个整数的序列 $ a $，满足 $ a_i \leq 10^9 $，在执行一个操作后，这个序列的数字总和一定会变小。 现在给你一个整数 $ n $，你需要构造一个长度为 $ n $ 的序列，使得它不满足上面的这个猜想。

题目描述

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).

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

3
2
512
3

输出样例 #1

YES
1 337
NO
YES
31 4 159

说明

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.