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.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.util.StringTokenizer;
  import java.util.Arrays;
  import java.util.ArrayList;
  import java.util.Comparator;
  import java.util.HashMap;
  import java.util.HashSet;
  import java.util.TreeSet;
  import java.util.TreeMap;
  import java.util.PriorityQueue;
  import java.util.Collections;
  
  import java.util.LinkedList;
  import java.util.Iterator;
  
  public class First {
  
      public static void main(String[] args) {
          FastScanner fs = new FastScanner();
          int T = fs.nextInt();
          for (int tt = 0; tt < T; tt++) {
  
              solve(fs);
          }
          
      }
      static void solve(FastScanner fs)
      {
          int n=fs.nextInt();
          long[] arr=takeLong(n, fs);
  
          long sum=0;
          for(int i=0;i<n;++i)
              sum+=(arr[i]);
  
          long total=((long)n*(n+1)/2);
  
          if(sum%total!=0)
          {
              pn("NO"); return;
          }
  
          long s=sum/total;
  
          ArrayList<Long> ls=new ArrayList<>();
  
          for(int i=1;i<n;++i)
          {
              ls.add(arr[i]-arr[i-1]);
          }
          ls.add(arr[0]-arr[n-1]);
  
          long[] temp=new long[n];
  
          for(int i=1;i<=n;++i)
          {
              int idx=i%n;
  
              temp[idx]=s-ls.get(i-1);
  
              if(temp[idx]%n!=0)
              {
                  pn("NO"); return;
              }
  
              temp[idx]/=n;
              if(temp[idx]<=0)
              {
                  pn("NO"); return;
              }
          }
          pn("YES");
          for(long ele: temp)
              p(ele+" ");
          pn("");
      }
      static int MOD=(int)(1e9+7);
      
      static long gcd(long a, long b) 
      {
          if (a == 0)
              return b;    
          return gcd(b%a, a);
      }
      static void pn(Object o) { System.out.println(o); } 
      static void p(Object o) { System.out.print(o); }
      static void flush() { System.out.flush(); }
  
      static void debugInt(int[] arr)
      {
          for(int i=0;i<arr.length;++i)
              System.out.print(arr[i]+" ");
          System.out.println();
      }
      static void debugIntInt(int[][] arr)
      {
          for(int i=0;i<arr.length;++i)
          {
              for(int j=0;j<arr[0].length;++j)
                  System.out.print(arr[i][j]+" ");
              System.out.println();
          }
          System.out.println();
      }
      static void debugLong(long[] arr)
      {
          for(int i=0;i<arr.length;++i)
              System.out.print(arr[i]+" ");
          System.out.println();
      }
      static void debugLongLong(long[][] arr)
      {
          for(int i=0;i<arr.length;++i)
          {
              for(int j=0;j<arr[0].length;++j)
                  System.out.print(arr[i][j]+" ");
              System.out.println();
          }
          System.out.println();
      }
      static long[] takeLong(int n, FastScanner fs)
      {
          long[] arr=new long[n];
          for(int i=0;i<n;++i)
              arr[i]=fs.nextLong();
          return arr;
      } 
      static long[][] takeLongLong(int m, int n, FastScanner fs)
      {
          long[][] arr=new long[m][n];
          for(int i=0;i<m;++i)
              for(int j=0;j<n;++j)
                  arr[i][j]=fs.nextLong();
          return arr;
      } 
      static int[] takeInt(int n, FastScanner fs)
      {
          int[] arr=new int[n];
          for(int i=0;i<n;++i)
              arr[i]=fs.nextInt();
          return arr;
      } 
      static int[][] takeIntInt(int m, int n, FastScanner fs)
      {
          int[][] arr=new int[m][n];
          for(int i=0;i<m;++i)
              for(int j=0;j<n;++j)
                  arr[i][j]=fs.nextInt();
          return arr;
      } 
      static void sort(int[] a) {
          ArrayList<Integer> l=new ArrayList<>();
          for (int i:a) l.add(i);
          Collections.sort(l);
          for (int i=0; i<a.length; i++) a[i]=l.get(i);
      }
      static boolean[] sieve()
      {
          int size=(int)(1e5+5);
          boolean[] isPrime=new boolean[size];
          Arrays.fill(isPrime, true);
          for(int i=2;i<size;++i)
              for(int j=2*i;isPrime[i]==true && j<size;j+=i)
                  isPrime[j]=false;
  
          return isPrime;
      }
      static class FastScanner {
          BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
          StringTokenizer st = new StringTokenizer("");
          String next() {
              while (!st.hasMoreTokens())
                  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());
          }
      }
  
  
  }
  class Pair
  {
      
  }