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 A {
      //--------------------------INPUT READER---------------------------------//
      static class fs {
          public BufferedReader br;
          StringTokenizer st = new StringTokenizer("");
  
          public fs() { this(System.in); }
          public fs(InputStream is) {
              br = new BufferedReader(new InputStreamReader(is));
          }
          String next() {
              while (!st.hasMoreTokens()) {
                  try { st = new StringTokenizer(br.readLine()); }
                  catch (IOException e) { e.printStackTrace(); }
              }
              return st.nextToken();
          }
  
          int ni() { return Integer.parseInt(next()); }
          long nl() { return Long.parseLong(next()); }
          double nd() { return Double.parseDouble(next()); }
          String ns() { return next(); }
  
          int[] na(long nn) {
              int n = (int) nn;
              int[] a = new int[n];
              for (int i = 0; i < n; i++) a[i] = ni();
              return a;
          }
  
          long[] nal(long nn) {
              int n = (int) nn;
              long[] l = new long[n];
              for(int i = 0; i < n; i++) l[i] = nl();
              return l;
          }
      }
      //-----------------------------------------------------------------------//
  
      //---------------------------PRINTER-------------------------------------//
      static class Printer {
          static PrintWriter w;
          public Printer() {this(System.out);}
          public Printer(OutputStream os) {
              w = new PrintWriter(os);
          }
          public void p(int i) {w.println(i);}
          public void p(long l) {w.println(l);}
          public void p(double d) {w.println(d);}
          public void p(String s) { w.println(s);}
          public void pr(int i) {w.print(i);}
          public void pr(long l) {w.print(l);}
          public void pr(double d) {w.print(d);}
          public void pr(String s) { w.print(s);}
          public void pl() {w.println();}
          public void close() {w.close();}
      }
      //-----------------------------------------------------------------------//
  
      //--------------------------VARIABLES------------------------------------//
      static fs sc = new fs();
      static OutputStream outputStream = System.out;
      static Printer w = new Printer(outputStream);
      static long lma = Long.MAX_VALUE, lmi = Long.MIN_VALUE;
      static long ima = Integer.MAX_VALUE, imi = Integer.MIN_VALUE;
      static long mod = 1000000007;
      //-----------------------------------------------------------------------//
  
      //--------------------------ADMIN_MODE-----------------------------------//
      private static void ADMIN_MODE() throws IOException {
          if (System.getProperty("ONLINE_JUDGE") == null) {
              w = new Printer(new FileOutputStream("output.txt"));
              sc = new fs(new FileInputStream("input.txt"));
          }
      }
      //-----------------------------------------------------------------------//
  
      //----------------------------START--------------------------------------//
      public static void main(String[] args)
              throws IOException {
  
          ADMIN_MODE();
  
          int t = sc.ni();while(t-->0)
              solve();
  
  
          w.close();
      }
  
      static void solve() throws IOException {
          int n = sc.ni();
          long[] arr = sc.nal(n);
          long[] res = new long[n];
          long contSum = (((long)n)*(n+1))/2;
          long sum = 0;
          for(long i: arr) {
              sum += i;
          }
          long q = sum/contSum;
          if(sum%contSum!=0) {
              w.p("NO");
              return;
          }
  
          for(int i = 0; i < n; i++) {
              long minus = arr[(i+1)%n]-q;
              if((arr[i]-minus)%n!=0) {
                  w.p("NO");
                  return;
              }
              res[(i+1)%n]=(arr[i]-minus)/n;
              if(res[(i+1)%n]<=0) {
                  w.p("NO");
                  return;
              }
          }
  
          w.p("YES");
          for(long i: res) {
              w.pr(i+" ");
          }
          w.pl();
      }
  
  }