write a go solution for E. Balancedtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a cyclic array a with n elements, where n is odd. In each operation, you can do the following:  Choose an index 1<=i<=n and increase a_i-1 by 1, a_i by 2, and a_i+1 by 1. The element before the first element is the last element because this is a cyclic array. A cyclic array is called balanced if all its elements are equal to each other.Find any sequence of operations to make this cyclic array balanced or determine that it is impossible. Please note that you do not have to minimize the number of operations.InputEach test consists of multiple test cases. The first line contains a single integer t (1<=t<=2*10^5) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n (1<=n<2*10^5, n is odd) — the length of the array a.The second line of each test case contains n integers a_1,a_2,ldots,a_n (1<=a_i<=10^6) — the elements of the array a.It is guaranteed that the sum of n over all test cases does not exceed 2*10^5.OutputFor each test case:   If it is impossible to make the cyclic array balanced, output -1.  Otherwise, output n integers v_1,v_2,ldots,v_n (0<=v_i<=10^18) — where v_i denotes the number of operations applied to index i. It can be proved that if any solution exists, then there exists a solution under the given constraints. If there are several solutions under the given constraints, output any of them. ExampleInput632 1 231 2 351 2 1 2 171 2 1 2 1 3 1910000 10000 10000 10000 10000 10001 10002 10001 10000110Output0 1 0 
2 1 0 
2 0 3 0 2 
4 2 7 0 8 0 6 
1 1 1 1 1 1 0 1 1 
0 
NoteIn the first test case:  After 1 operation applied to index i=2, the array a=[3,3,3]. In the second test case:  After 2 operations applied to index i=1, the array a=[5,4,5]. After 1 operation applied to index i=2, the array a=[6,6,6]. In the third test case:  After 2 operations applied to index i=1, the array a=[5,4,1,2,3]. After 3 operations applied to index i=3, the array a=[5,7,7,5,3]. After 2 operations applied to index i=5, the array a=[7,7,7,7,7].. Output only the code with no comments, explanation, or additional text.