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.lang.*;
   import java.io.*;
  
  public class E_Singers_Tour
   {
       static int M = 1_000_000_007;
       static final PrintWriter out =new PrintWriter(System.out);
       static final FastReader fs = new FastReader();
       static boolean prime[];
       public static void main (String[] args) throws java.lang.Exception
       {
             
             int t= fs.nextInt();
            aaa: for(int i=0;i<t;i++)
             {
                 int n= fs.nextInt();
                 long a[]=fs.arrayIn(n);
                 long sum=0;
                 long sumn=(long)n*(long)(n+1);
                 sumn=sumn/2;
                 for(int j=0;j<n;j++){
                     sum+=(long)a[j];
                 }
                 if(sum%sumn!=0){
                     out.println("NO");
                     continue aaa;
                 }
                 long suma=sum/sumn;
                 int ans[]=new int[n];
                 for(int j=1;j<n;j++){
                     long kl=(long)a[j-1]-(long)a[j]+suma;
                     if(kl<=0||kl%(long)n!=0){
                      out.println("NO");
                      continue aaa;
                     }
                     ans[j]=(int)(kl/(long)n);
                 }
                 long kl=(long)a[n-1]-(long)a[0]+suma;
                     if(kl<=0||kl%(long)n!=0){
                      out.println("NO");
                      continue aaa;
                     }
                     ans[0]=(int)(kl/(long)n);
                     out.println("YES");
                     for(int j=0;j<n;j++){
                         out.print(ans[j]+" ");
                     }
                     out.println();
             }
             out.flush();
    }
    public static long power(long x, long y)
    {
        long temp;
        if (y == 0)
            return 1;
        temp = power(x, y / 2);
  
        if (y % 2 == 0)
            return modMult(temp,temp);
        else {
            if (y > 0)
                return modMult(x,modMult(temp,temp));
            else
                return (modMult(temp,temp)) / x;
        }
    }
    static void sieveOfEratosthenes(int n)
      {
           prime = new boolean[n + 1];
          for (int i = 0; i <= n; i++)
              prime[i] = true;
              prime[0]=false;
              if(1<=n)
              prime[1]=false;
          for (int p = 2; p * p <= n; p++)
          {
              
              if (prime[p] == true)
              {
                 
                  for (int i = p * p; i <= n; i += p)
                      prime[i] = false;
              }
          }
      }
           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;
           }
   long [] arrayIn(int n) throws IOException
       {
           long  arr[] = new long[n];
           for(int i=0; i<n; i++)
           {
               arr[i] = nextLong();
           }
           return arr;
       }
       }
       
       public static class Pairs implements Comparable<Pairs>
       {
           int value,index;
           Pairs(int value, int index)
           {
               this.value = value;
               this.index = index;
           }
           public int compareTo(Pairs p)
           {
               return Integer.compare(this.value, p.value);
           }
       }
       static final Random random = new Random();
    
       static void ruffleSort(int arr[])
       {
           int n = arr.length;
           for(int i=0; i<n; i++)
           {
               int j = random.nextInt(n),temp = arr[j];
               arr[j] = arr[i];
               arr[i] = temp;
           }
           Arrays.sort(arr);
       }
       static long nCk(int n, int k) {
           return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
       }
    
       static long fact (long n) {
    
           long fact =1;
           for(int i=1; i<=n; i++) {
               fact = modMult(fact,i);
           }
           return fact%M;
       }
    
       static long modMult(long a,long b) {
           return a*b%M;
       }
    
       static long fastexp(long x, int y){
           if(y==1) return x;
    
           long ans = fastexp(x,y/2);
           if(y%2 == 0) return modMult(ans,ans);
           else return modMult(ans,modMult(ans,x));
       }
   }