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.io.*;
  import java.util.*;
  
  public class Codeforces
  {
      public static void main(String args[])throws Exception
      {
          BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
          StringBuilder sb=new StringBuilder();
          int t=Integer.parseInt(bu.readLine());
          while(t-->0)
          {
              int n=Integer.parseInt(bu.readLine());
              String s[]=bu.readLine().split(" ");
              int i,a[]=new int[n],sum[]=new int[n];
              for(i=0;i<n;i++)
              a[i]=Integer.parseInt(s[i]);    //a[1]=a1+na2+(n-1)a3+...+2an, a[2]= 2a1+a2+...+3an
              for(i=0;i<n;i++) sum[i]=a[i]-a[(i-1+n)%n];  //sum[i]=total sum-n*ans[i]
  
              boolean ok=true;
              long total=0,nn=1l*n*(n+1)/2;
              for(i=0;i<n;i++) total+=a[i];   //sum*n*(n+1)/2
              if(total%nn!=0) ok=false;
              total/=nn;
  
              long ans[]=new long[n];
              for(i=0;i<n && ok;i++)
              {
                  ans[i]=-total+sum[i];
                  ans[i]=-ans[i];
                  if(ans[i]%n!=0) ok=false;
                  ans[i]/=n;
                  if(ans[i]<=0) ok=false;
              }
              if(ok)
              {
                  sb.append("YES\n");
                  for(i=0;i<n;i++) sb.append(ans[i]+" ");
              }
              else sb.append("NO");
              sb.append("\n");
          }
          System.out.print(sb);
      }
  }