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 Main {
      static FastScanner sc = new FastScanner(System.in);
      static PrintWriter pw = new PrintWriter(System.out);
      static StringBuilder sb = new StringBuilder();
      static long mod = (long) 1e9 + 7;
      static long[] pow = new long[50000];
      public static void main(String[] args) throws Exception {
          pow[1] = 1;
          for(int i = 2; i < 50000; i++){
              pow[i] = pow[i-1]+i;
          }
          int N = sc.nextInt();
          for(int i = 0 ; i < N; i++) solve();
          pw.flush();
      }
  
      public static void solve() {
          sb.setLength(0);
          int N = sc.nextInt();
          if(N == 1){
              pw.println("YES");
              pw.println(sc.nextLong());
              return;
          }
          long total = 0;
          long rev = 0;
          long[] inc = new long[N];
          long[] A = sc.nextLongArray(N);
          for(int i = 0; i < N; i++){
              total += A[i];
              if(i == 0){
                  rev += A[i] - A[N-1];
                  inc[i] = A[i] - A[N-1];
              }else{
                  rev += A[i] - A[i-1];
                  inc[i] = A[i] - A[i-1];
              }
          }
          if(rev != 0){
              pw.println("NO");
              return;
          }else{
              for(int i = 0; i < N; i++){
                  long tmp = total-(inc[i]*pow[N]);
                  long cum = (pow[N]*N);
                  if(tmp % cum != 0 || tmp <= 0){
                      pw.println("NO");
                      return;
                  }else{
                      sb.append(tmp / cum).append(" ");
                  }
              }
              pw.println("YES");
              pw.println(sb.toString().trim());
          }
      }
      
      static class GeekInteger {
          public static void save_sort(int[] array) {
              shuffle(array);
              Arrays.sort(array);
          }
  
          public static int[] shuffle(int[] array) {
              int n = array.length;
              Random random = new Random();
              for (int i = 0, j; i < n; i++) {
                  j = i + random.nextInt(n - i);
                  int randomElement = array[j];
                  array[j] = array[i];
                  array[i] = randomElement;
              }
              return array;
          }
  
          public static void save_sort(long[] array) {
              shuffle(array);
              Arrays.sort(array);
          }
  
          public static long[] shuffle(long[] array) {
              int n = array.length;
              Random random = new Random();
              for (int i = 0, j; i < n; i++) {
                  j = i + random.nextInt(n - i);
                  long randomElement = array[j];
                  array[j] = array[i];
                  array[i] = randomElement;
              }
              return array;
          }
  
      }
  }
  
  class FastScanner {
      private BufferedReader reader = null;
      private StringTokenizer tokenizer = null;
  
      public FastScanner(InputStream in) {
          reader = new BufferedReader(new InputStreamReader(in));
          tokenizer = null;
      }
  
      public FastScanner(FileReader in) {
          reader = new BufferedReader(in);
          tokenizer = null;
      }
  
      public String next() {
          if (tokenizer == null || !tokenizer.hasMoreTokens()) {
              try {
                  tokenizer = new StringTokenizer(reader.readLine());
              } catch (IOException e) {
                  throw new RuntimeException(e);
              }
          }
          return tokenizer.nextToken();
      }
  
      public String nextLine() {
          if (tokenizer == null || !tokenizer.hasMoreTokens()) {
              try {
                  return reader.readLine();
              } catch (IOException e) {
                  throw new RuntimeException(e);
              }
          }
          return tokenizer.nextToken("\n");
      }
  
      public long nextLong() {
          return Long.parseLong(next());
      }
  
      public int nextInt() {
          return Integer.parseInt(next());
      }
  
      public double nextDouble() {
          return Double.parseDouble(next());
      }
  
      public String[] nextArray(int n) {
          String[] a = new String[n];
          for (int i = 0; i < n; i++)
              a[i] = next();
          return a;
      }
  
      public int[] nextIntArray(int n) {
          int[] a = new int[n];
          for (int i = 0; i < n; i++)
              a[i] = nextInt();
          return a;
      }
  
      public long[] nextLongArray(int n) {
          long[] a = new long[n];
          for (int i = 0; i < n; i++)
              a[i] = nextLong();
          return a;
      }
  }
  