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.OutputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.PrintWriter;
  import java.util.*;
  import java.io.IOException;
  import java.io.BufferedReader;
  import java.io.InputStreamReader;
  import java.io.InputStream;
  
  public class Main {
  
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          PrintWriter out = new PrintWriter(outputStream);
          TaskA solver = new TaskA();
          int t;
          t = in.nextInt();
          //t = 1;
          while (t > 0) {
              solver.call(in,out);
              t--;
          }
          out.close();
      }
  
      static class TaskA {
          public void call(InputReader in, PrintWriter out) {
              int n;
              n = in.nextInt();
  
              int[] arr = new int[n];
              long sum = 0, k = ((long) n*(long) (n + 1))/2L;
              for (int i = 0; i < n; i++) {
                  arr[i] = in.nextInt();
                  sum += arr[i];
              }
              if(sum%k!=0){
                  out.println("NO");
              }
              else{
                  k = sum/k;
  
                  long[] ans = new long[n];
                  for (int i = 1; i < n; i++) {
  
                      if((k - arr[i] + arr[i - 1]) % n!=0){
                          out.println("NO");
                          return;
                      }
                      ans[i] = (k - arr[i] + arr[i - 1]) / n;
                  }
  
                  if((k - arr[0] + arr[n - 1]) % n!=0){
                      out.println("NO");
                      return;
                  }
                  ans[0] = (k - arr[0] + arr[n - 1]) / n;
  
                  for (int i = 0; i < n; i++) {
                      if(ans[i]<=0){
                          out.println("NO");
                          return;
                      }
                  }
                  out.println("YES");
                  for (Long g:ans) {
                      out.print(g+" ");
                  }
                  out.println();
              }
  
  
  
  
  
          }
      }
  
      static int gcd(int a, int b)
      {
          if (a == 0)
              return b;
          return gcd(b % a, a);
      }
  
      static int lcm(int a, int b)
      {
          return (a / gcd(a, b)) * b;
      }
  
      static class answer implements Comparable<answer>{
          int a, b;
  
          public answer(int a, int b) {
              this.a = a;
              this.b = b;
          }
  
          @Override
          public int compareTo(answer o) {
              return o.a - this.a;
          }
      }
  
      static class arrayListClass {
          ArrayList<Integer> arrayList2 ;
  
          public arrayListClass(ArrayList<Integer> arrayList) {
              this.arrayList2 = arrayList;
          }
      }
  
      static long gcd(long a, long b)
      {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
  
      static void sort(long[] a) {
          ArrayList<Long> l=new ArrayList<>();
          for (long i:a) l.add(i);
          Collections.sort(l);
          for (int i=0; i<a.length; i++) a[i]=l.get(i);
      }
  
      static final Random random=new Random();
  
      static void shuffleSort(int[] a) {
          int n=a.length;
          for (int i=0; i<n; i++) {
              int oi=random.nextInt(n), temp=a[oi];
              a[oi]=a[i]; a[i]=temp;
          }
          Arrays.sort(a);
      }
  
      static class InputReader {
          public BufferedReader reader;
          public StringTokenizer tokenizer;
  
          public InputReader(InputStream stream) {
              reader = new BufferedReader(new InputStreamReader(stream), 32768);
              tokenizer = null;
          }
  
          public String next() {
              while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                  try {
                      tokenizer = new StringTokenizer(reader.readLine());
                  } catch (IOException e) {
                      throw new RuntimeException(e);
                  }
              }
              return tokenizer.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
          public long nextLong(){
              return Long.parseLong(next());
          }
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
      }
  }