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 Solution {
      static class FastReader {
          BufferedReader br;
          StringTokenizer st;
          public FastReader() {
              br = new BufferedReader(new InputStreamReader(System.in));
          }
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
          int nextInt() {
              return Integer.parseInt(next());
          }
          long nextLong() {
              return Long.parseLong(next());
          }
          double nextDouble() {
              return Double.parseDouble(next());
          }
          String nextLine() {
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }
      }
      static void sort(int a[]){ // int -> long
          ArrayList<Integer> arr=new ArrayList<>(); // Integer -> Long
          for(int i=0;i<a.length;i++)
          arr.add(a[i]);
          Collections.sort(arr);
          for(int i=0;i<a.length;i++)
          a[i]=arr.get(i);
          
      }
      private static long gcd(long a, long b){
          if(b==0)return a;
          return gcd(b,a%b);
      }
      private static long pow(long x,long y){
          if(y==0)return 1;
          long temp = pow(x, y/2);
          if(y%2==1){
              return x*temp*temp;
          }
          else{
              return temp*temp;
          }
      }
      static int log(long n){
          int res = 0;
          while(n>0){
              res++;
              n/=2;
          }
          return res;
      }
  
      static int mod = (int)1e9+7;
      static PrintWriter out;
      static FastReader sc ;
      public static void main(String[] args) throws IOException {
          sc = new FastReader();
          out = new PrintWriter(System.out);
          // primes();
          // ================================ //
          int test = sc.nextInt();
          while (test-- > 0) {
              int n = sc.nextInt();
              long[]arr =new long[n];
              for(int i=0;i<n;i++){
                  arr[i] = sc.nextInt();
              }
              solver(arr, n);
          }
          // ================================ //
          // int n = sc.nextInt();
          // solver();
          // ================================ //
          out.flush();
      }
  
      public static void solver(long[]arr, int n) {
          long sum = 0;
          for(int i=0;i<n;i++)sum+=arr[i];
          if(sum%((long)n*(n+1)/2)!=0){
              out.println("NO");
              return;
          }
          sum = sum/((long)n*(n+1)/2);
          long res[] = new long[n];
          for(int i=0;i<n;i++){
              if(i==0){
                  res[i] = (arr[n-1]-arr[i]+sum)/n;
                  if(res[i]<1 || (arr[n-1]-arr[i]+sum)%n!=0 || res[i]>(long)1e9){
                      out.println("NO");
                      return;
                  }
              }
              else{
                  res[i] = (arr[i-1]-arr[i]+sum)/n;
                  if(res[i]<1 || (arr[i-1]-arr[i]+sum)%n!=0 || res[i]>(long)1e9){
                      out.println("NO");
                      return;
                  }
              }
          }
          // if(!check(res, arr)){
          //     out.println("NO");
          //     return;
          // }
          out.println("YES");
          for(long e: res)out.print(e+" ");
          out.println( );
      }
      static boolean check(long[]res, long[] og){
          int n = res.length;
          long[] arr = new long[n];
          for(int i=0;i<n;i++){
              for(int j=0;j<n;j++){
                  int m = (i+j)%n;
                  arr[i]+=res[m]*(j+1);
                  System.out.println(arr[i]+"__"+    og[i]);
              }
          }
  
          for(int i=0;i<n;i++){
              if(og[i]!=arr[i]){
                  return false;
              }
          }
          return true;
      }
  }
  