description: n towns are arranged in a circle sequentially. The towns are numbered from 1 to n in clockwise order. In the i-th town, there lives a singer with a repertoire of a_i minutes for each i ∈ [1, n].
  
  Each singer visited all n towns in clockwise order, starting with the town he lives in, and gave exactly one concert in each town. In addition, in each town, the i-th singer got inspired and came up with a song that lasts a_i minutes. The song was added to his repertoire so that he could perform it in the rest of the cities.
  
  Hence, for the i-th singer, the concert in the i-th town will last a_i minutes, in the (i + 1)-th town the concert will last 2 ⋅ a_i minutes, ..., in the ((i + k) mod n + 1)-th town the duration of the concert will be (k + 2) ⋅ a_i, ..., in the town ((i + n - 2) mod n + 1) — n ⋅ a_i minutes.
  
  You are given an array of b integer numbers, where b_i is the total duration of concerts in the i-th town. Reconstruct any correct sequence of positive integers a or say that it is impossible.
  
  Input
  
  The first line contains one integer t (1 ≤ t ≤ 10^3) — the number of test cases. Then the test cases follow.
  
  Each test case consists of two lines. The first line contains a single integer n (1 ≤ n ≤ 4 ⋅ 10^4) — the number of cities. The second line contains n integers b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^{9}) — the total duration of concerts in i-th city.
  
  The sum of n over all test cases does not exceed 2 ⋅ 10^5.
  
  Output
  
  For each test case, print the answer as follows:
  
  If there is no suitable sequence a, print NO. Otherwise, on the first line print YES, on the next line print the sequence a_1, a_2, ..., a_n of n integers, where a_i (1 ≤ a_i ≤ 10^{9}) is the initial duration of repertoire of the i-th singer. If there are multiple answers, print any of them.
  
  Example
  
  Input
  
  
  4
  3
  12 16 14
  1
  1
  3
  1 2 3
  6
  81 75 75 93 93 87
  
  
  Output
  
  
  YES
  3 1 3 
  YES
  1 
  NO
  YES
  5 5 4 1 4 5 
  
  Note
  
  Let's consider the 1-st test case of the example:
  
    1. the 1-st singer in the 1-st city will give a concert for 3 minutes, in the 2-nd — for 6 minutes, in the 3-rd — for 9 minutes; 
    2. the 2-nd singer in the 1-st city will give a concert for 3 minutes, in the 2-nd — for 1 minute, in the 3-rd - for 2 minutes; 
    3. the 3-rd singer in the 1-st city will give a concert for 6 minutes, in the 2-nd — for 9 minutes, in the 3-rd — for 3 minutes. 
solution: import java.util.*;
  import java.io.*;
  
  public class Solution {
      
      public static void main(String[] args) throws IOException {
  
          BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  
          int t = Integer.parseInt(br.readLine());
  
          BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
  
          StringTokenizer st;
  
          while (t-- > 0) {
  
              int n = Integer.parseInt(br.readLine());
  
              st = new StringTokenizer(br.readLine());
  
              int arr[] = new int[n];
              long arr2[] = new long[n];
  
              long sumb = 0;
              for(int i = 0; i < n; i++)
              {
              int e = Integer.parseInt(st.nextToken());
              arr[i] = e;
              sumb+=e;
              }
  
              long suma = 0;
              long nt = n * (n+1);
              nt/=2;
  
              if(sumb % nt != 0)
              {
                  output.write("NO\n");
                  continue;
              }
  
              suma = sumb / nt;
  
              int flag = 0;
              
              for(int i = 0; i < n; i++)
              {
                  long diff = arr[i] - arr[(i+1) % n] + suma;
                  if(diff % n != 0 || diff <= 0)
                      flag = 1;
                  
                  arr2[(i+1) % n] = diff / n;
              }
  
              if(flag == 1)
              {
                  output.write("NO\n");
                  continue;
              }
  
              output.write("YES\n");
              for(long i : arr2)
                  output.write(i + " ");
  
              output.write("\n");
  
  
  
  
              // int k = Integer.parseInt(st.nextToken());
  
              // char arr[] = br.readLine().toCharArray();
  
              // output.write();
              // int n = Integer.parseInt(st.nextToken());
  
              // HashMap<Character, Integer> map = new HashMap<Character, Integer>();
  
              // if
              // output.write("YES\n");
              // else
              // output.write("NO\n");
  
              // long a = Long.parseLong(st.nextToken());
              // long b = Long.parseLong(st.nextToken());
  
              // if(flag == 1)
              // output.write("NO\n");
              // else
              // output.write("YES\n" + x + " " + y + " " + z + "\n");
  
              // output.write(n+ "\n");
  
          }
  
          output.flush();
  
      }
  
  }