CF1779B.MKnez's ConstructiveForces Task

MKnez wants to construct an array $s_1,s_2, \ldots , s_n$ satisfying the following conditions:

• Each element is an integer number different from $0$;
• For each pair of adjacent elements their sum is equal to the sum of the whole array.

More formally, $s_i \neq 0$ must hold for each $1 \leq i \leq n$. Moreover, it must hold that $s_1 + s_2 + \cdots + s_n = s_i + s_{i+1}$ for each $1 \leq i \lt n$.

Help MKnez to construct an array with these properties or determine that it does not exist.

MKnez 想要构造一个数组 $s_1,s_2, \ldots , s_n$，满足以下条件：

• 每个元素均为非零整数；
• 每一对相邻元素之和等于整个数组所有元素的总和。

更形式化地说，对每个 $1 \leq i \leq n$，必须满足 $s_i \neq 0$；此外，对每个 $1 \leq i \lt n$，必须满足 $s_1 + s_2 + \cdots + s_n = s_i + s_{i+1}$。

请帮助 MKnez 构造出满足这些性质的数组，或判断这样的数组不存在。

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.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \leq t \leq 100$）。随后是测试用例的描述。

每个测试用例仅有一行，包含一个整数 $n$（$2 \leq n \leq 1000$）—— 数组的长度。

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.

对于每个测试用例，如果存在长度为 $n$ 且满足条件的数组，则输出 "YES"；否则输出 "NO"。若答案为 "YES"，则在下一行输出一个满足条件的序列 $s_1,s_2, \ldots, s_n$。序列中每个元素都必须是非零整数，且取值范围为 $[-5000,5000]$，即对每个 $1 \leq i \leq n$，需满足 $-5000 \leq s_i \leq 5000$ 且 $s_i \neq 0$。

可以证明：若解存在，则必存在一个解满足上述范围限制。

若存在多个正确答案，输出任意一个即可。

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".

在第一个测试用例中，$[9,5]$ 是一个合法的答案，因为 $9+5$（两个相邻元素 $s_1+s_2$ 的和）等于 $9+5$（所有元素的总和）。其他合法解还包括 $[6,-9], [-1,-2], [-5000,5000], \ldots$

在第二个测试用例中，我们说明为何某些数组不满足约束条件：

• $[1,1,1]$ — $s_1+s_2 = 1+1 = 2$，而 $s_1+s_2+s_3=1+1+1 = 3$，二者不相等；
• $[1,-1,1]$ — $s_1+s_2=1+(-1)=0$，而 $s_1+s_2+s_3=1+(-1)+1 = 1$，二者不相等；
• $[0,0,0]$ — 数组 $s$ 中不能包含 $0$。

这并非严格证明，但可以证明该测试用例的答案为 “NO”。