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.*;
  import java.util.*;
   
  public class cf {
   
      public static void main(String[] args){
   
          FastScanner sc = new FastScanner();
          int x = sc.nextInt();
          //int x=1;
          while(x-- > 0){
              int n=sc.nextInt();
              int []arr=new int[n];
              long sum=0L;
              for(int i=0;i<n;i++){
                  arr[i]=sc.nextInt();
                  sum+=arr[i];
              }
              int y=n*(n+1)/2;
              ArrayList<Integer> a=new ArrayList<>();
              boolean check=true;
              if(sum%y!=0){
                  System.out.println("NO");
              }
              else{
                  sum=sum/y;
                  for(int i=0;i<n;i++){
                      int dif=0;
                      if(i==0){
                          dif=arr[0]-arr[n-1];
  
                      }
                      else{
                          dif=arr[i]-arr[i-1];
                      }
                      if((sum-dif)%n!=0 || sum-dif<=0){
                          System.out.println("NO");
                          check =false;
                          break;
                      }
                      else{
                          a.add((int)(sum-dif)/n);
                      }
                  }
                  if(check==true){
                      System.out.println("YES");
                      for(int i=0;i<n;i++){
                          System.out.print(a.get(i)+" ");
                      }
                      System.out.println();
                  }
              }
  
  
  
  
  
  
              
              
  
  
  
              
              
  
          }
          
  
      }
      public static long gcd(long a,long b){
          if(b == 0){
              return a;
          }
          return gcd(b,a%b);
      }               
              
  }
  /////////////////////////////////////////////////////////////
  //BINARY SEARCH
  /*Arrays.binarySearch(arr,key);
  if key--> present 
      return index
  else 
      return -(index where it would be inserted)-1*/
  
  
  //////////////////////////////////////////////////////////////
   
  
  
  /*  VALUE JUST GREATER THAN X  
   find_min(int[]arr,int x){
      int l=-1;
      int r=arr.length;
      while(r>l+1){
          int mid=(l+r)/2;
          if(arr[mid]<x){
              l=mid;
          }
          else{
              r=mid;
          }
      }
      return r;
   }
      VALUE JUST SMALLER THAN X
    find_max(int[]arr,int x){
      int l=-1;
      int r=arr.length;
      while(r>l+1){
          int mid=(l+r)/2;
          if(arr[mid]<=x){
              l=mid;
          }
          else{
              r=mid;
          }
      }
      return l;
   }  
     */ 
      
   
  
  
  //////////////////////////////////////////////////////////////
  // LCM AND GCD
  /*
      public static int gcd(int a,int b){
          if(b == 0){
              return a;
          }
          return gcd(b,a%b);
      }
   
      public static int lcm(int a,int b){
           return (a / gcd(a, b)) * b;
      }*/
  
  
  ///////////////////////////////////////////////////////////////////////////////////
  
  //Iterator
  
  
  
  /*Iterator iterator = object.iterator();
   
          while (iterator.hasNext()) {
              System.out.print(iterator.next() + " ");
          }*/
  ///////////////////////////////////////////////////////////////////////////////////
  
  
  class FastScanner
  {
      //I don't understand how this works lmao
      private int BS = 1 << 16;
      private char NC = (char) 0;
      private byte[] buf = new byte[BS];
      private int bId = 0, size = 0;
      private char c = NC;
      private double cnt = 1;
      private BufferedInputStream in;
   
      public FastScanner() {
          in = new BufferedInputStream(System.in, BS);
      }
   
      public FastScanner(String s) {
          try {
              in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
          } catch (Exception e) {
              in = new BufferedInputStream(System.in, BS);
          }
      }
   
      public char getChar() {
          while (bId == size) {
              try {
                  size = in.read(buf);
              } catch (Exception e) {
                  return NC;
              }
              if (size == -1) return NC;
              bId = 0;
          }
          return (char) buf[bId++];
      }
   
      public int nextInt() {
          return (int) nextLong();
      }
   
      public int[] nextInts(int N) {
          int[] res = new int[N];
          for (int i = 0; i < N; i++) {
              res[i] = (int) nextLong();
          }
          return res;
      }
   
      public long[] nextLongs(int N) {
          long[] res = new long[N];
          for (int i = 0; i < N; i++) {
              res[i] = nextLong();
          }
          return res;
      }
   
      public long nextLong() {
          cnt = 1;
          boolean neg = false;
          if (c == NC) c = getChar();
          for (; (c < '0' || c > '9'); c = getChar()) {
              if (c == '-') neg = true;
          }
          long res = 0;
          for (; c >= '0' && c <= '9'; c = getChar()) {
              res = (res << 3) + (res << 1) + c - '0';
              cnt *= 10;
          }
          return neg ? -res : res;
      }
   
      public double nextDouble() {
          double cur = nextLong();
          return c != '.' ? cur : cur + nextLong() / cnt;
      }
   
      public double[] nextDoubles(int N) {
          double[] res = new double[N];
          for (int i = 0; i < N; i++) {
              res[i] = nextDouble();
          }
          return res;
      }
   
      public String next() {
          StringBuilder res = new StringBuilder();
          while (c <= 32) c = getChar();
          while (c > 32) {
              res.append(c);
              c = getChar();
          }
          return res.toString();
      }
   
      public String nextLine() {
          StringBuilder res = new StringBuilder();
          while (c <= 32) c = getChar();
          while (c != '\n') {
              res.append(c);
              c = getChar();
          }
          return res.toString();
      }
   
      public boolean hasNext() {
          if (c > 32) return true;
          while (true) {
              c = getChar();
              if (c == NC) return false;
              else if (c > 32) return true;
          }
      }
  }
  
  