B. MKnez's ConstructiveForces Tasktime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputMKnez 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 < n.Help MKnez to construct an array with these properties or determine that it does not exist.InputEach 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.OutputFor 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. ExampleInput
2
2
3
Output
YES
9 5
NO
NoteIn 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], \ldotsFor 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".
2
2
3

YES 9 5 NO 
['constructive algorithms', 'math', '*900']