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.*;
  
  public class E_Singers_Tour{
  
      static int N = 40010;
      static int n;
      static long[] a = new long[N];
      static long[] b = new long[N];
    
      public static void main(String[] args){
      
          Scanner sc = new Scanner(System.in);
          int T = sc.nextInt();
          while(T-- > 0){
              n = sc.nextInt();
              for(int i = 1; i <= n; i++) b[i] = sc.nextLong();
  
              if(slover()){
                  System.out.println("YES");
                  for(int i = 1; i <= n; i++){
                      System.out.print(a[i] + " ");
                  }
                  System.out.println();
              }else{
                  System.out.println("NO");
              }
          }
      }
  
      static boolean slover(){
          
          long l =  0;
          for(int i = 1; i <= n; i++) l += i;
          long sum = 0;
          for(int i = 1; i <= n; i++) sum  += b[i];
          if(sum % l != 0) return false;
          long bSum = sum / l;
  
          // 求a[1]
          if((b[n] - b[1] + bSum) <= 0 || (b[n] - b[1] + bSum) % n != 0) return false;
          a[1] = (b[n] - b[1] + bSum) / n;
          
          // 求a[2], ... , a[n]
          for(int i = 2; i <= n; i++){
              if((b[i - 1] - b[i] + bSum) % n != 0) return false;
              if((b[i - 1] - b[i] + bSum) <= 0 || (b[i - 1] - b[i] + bSum) % n != 0) return false;
              // System.out.println("----" + (b[3] - b[1] + bSum) + " l:" + l);
              a[i] = (b[i - 1] - b[i] + bSum) / n;
          }
          
          return true;
      }
  }