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: // हर हर महादेव
  import java.util.*;
  import java.lang.*;
  import java.io.*;
  import java.math.BigInteger;
  import java.text.DecimalFormat;
  
  public final class Solution {
  
      static int inf = Integer.MAX_VALUE;
      static long mod = 1000000000 + 7;
  
   static void ne(Scanner sc, BufferedWriter op) throws Exception { 
      int n=sc.nextInt();
      long[] arr= new long[n];
      long sum=0;
      for(int i=0;i<n;i++){
          arr[i]=sc.nextLong();
          sum+=arr[i];
      }
      if(n==1){
          op.write("Yes\n"+arr[0]+"\n");
          return;
      }
      long ns=((long)n*((long)n+1))/2L;
      if(sum%ns==0){
       long ss=sum/ns;
           boolean f=true;
           ArrayList<Long> list= new ArrayList<>();
           for(int i=1;i<n;i++){
               long nume=((arr[i-1]-arr[i]))+ss;
               if(nume%n!=0){
                   f=false;
                   break;
               }
               long val=nume/(long)n;
               list.add(val);
           }
        long fis=(arr[n-1]-arr[0])+ss;
        if(fis%n!=0){
            f=false;
        }
          fis=fis/n;
          
           if(fis<=0){
               f=false;
  
           }
           for(int i=0;i<list.size();i++){
               if(list.get(i)<=0){
                  f=false;
                  break;
               }
           }
           if(f){
               op.write("Yes\n"+fis+" ");
               for(int i=0;i<list.size();i++){
                   op.write(list.get(i)+" ");
               }
               op.write("\n");
               return;
           }
  
          op.write("No\n");
      }else{
          op.write("No\n");
      }
      
           
   }
  
      public static void main(String[] args) throws Exception {
          BufferedWriter op = new BufferedWriter(new OutputStreamWriter(System.out));
          // Reader sc = new Reader();
          Scanner sc= new Scanner(System.in);
          int t = sc.nextInt();
          while (t-->0){ ne(sc, op); }
          
          // ne(sc,op);
             
                     
          op.flush();
      }
  
      static void print(Object o) {
          System.out.println(String.valueOf(o));
      }
      static int[] toIntArr(String s){
          int[] val= new int[s.length()];
          for(int i=0;i<s.length();i++){
              val[i]=s.charAt(i)-'a';
          }
          return val;
      }
  
      static void  sort(int[] arr){
          ArrayList<Integer> list= new ArrayList<>();
          for(int i=0;i<arr.length;i++){
              list.add(arr[i]);
  
          }
          Collections.sort(list);
          for(int i=0;i<arr.length;i++){
              arr[i]=list.get(i);
          }
      }
         static void  sort(long[] arr){
          ArrayList<Long> list= new ArrayList<>();
          for(int i=0;i<arr.length;i++){
              list.add(arr[i]);
  
          }
          Collections.sort(list);
          for(int i=0;i<arr.length;i++){
              arr[i]=list.get(i);
          }
      }
  
  }
  
  
  
  // return -1 to put no ahed in array
  class pair {
      int  xx;
      int yy;
      pair(int xx, int yy ) {
          this.xx = xx;
          this.yy = yy;
      }
  }
  
  
  class sortY implements Comparator<pair> {
      public int compare(pair p1, pair p2) {
          if (p1.yy > p2.yy) {
              return 1;
          } else if (p1.yy == p2.yy) {
              if (p1.xx > p2.xx) {
                  return 1;
              } else if (p1.xx < p2.xx) {
                  return -1;
              }
              return 0;
  
          }
          return -1;
      }
  }
  
  class sortX implements Comparator<pair> {
      public int compare(pair p1, pair p2) {
          if (p1.xx > p2.xx) {
              return 1;
          } else if (p1.xx == p2.xx) {
              if (p1.yy > p2.yy) {
                  return 1;
              } else if (p1.yy < p2.yy) {
                  return -1;
              }
              return 0;
  
          }
          return -1;
      }
  }
  
  class debug {
  
      static void print1d(long[] arr) {
          System.out.println();
          for (int i = 0; i < arr.length; i++) {
              System.out.print(arr[i] + " ");
          }
  
      }
  
      static void print1d(int[] arr) {
          System.out.println();
          for (int i = 0; i < arr.length; i++) {
              System.out.println(i+" = "+arr[i]);
          }
  
      }
  
      static void print1d(boolean[] arr) {
          System.out.println();
          for (int i = 0; i < arr.length; i++) {
              System.out.println(i + "= " + arr[i]);
          }
  
      }
  
      static void print2d(int[][] arr) {
          System.out.println();
          int n = arr.length;
          int n2 = arr[0].length;
          for (int i = 0; i < n; i++) {
              for (int j = 0; j < n2; j++) {
                  System.out.print(arr[i][j] + " ");
              }
              System.out.println();
          }
  
      }
  
      static void print2d(long[][] arr) {
          System.out.println();
          int n = arr.length;
          int n2 = arr[0].length;
          for (int i = 0; i < n; i++) {
              for (int j = 0; j < n2; j++) {
                  System.out.print(arr[i][j] + " ");
              }
              System.out.println();
          }
  
      }
       static void printPair(ArrayList<pair> list) {
          if(list.size()==0){
              System.out.println("empty list");
              return;
          }
         System.out.println();
         for(int i=0;i<list.size();i++){
            System.out.println(list.get(i).xx+"-"+list.get(i).yy);
         }
      }
  
  }
  
  class Reader {
      final private int BUFFER_SIZE = 1 << 16;
      private DataInputStream din;
      private byte[] buffer;
      private int bufferPointer, bytesRead;
  
      public Reader() {
          din = new DataInputStream(System.in);
          buffer = new byte[BUFFER_SIZE];
          bufferPointer = bytesRead = 0;
      }
  
      public Reader(String file_name) throws IOException {
          din = new DataInputStream(new FileInputStream(file_name));
          buffer = new byte[BUFFER_SIZE];
          bufferPointer = bytesRead = 0;
      }
  
      public String readLine() throws IOException {
          byte[] buf = new byte[64]; // line length
          int cnt = 0, c;
          while ((c = read()) != -1) {
              if (c == '\n') {
                  if (cnt != 0) {
                      break;
                  } else {
                      continue;
                  }
              }
              buf[cnt++] = (byte) c;
          }
          return new String(buf, 0, cnt);
      }
  
      public int nextInt() throws IOException {
          int ret = 0;
          byte c = read();
          while (c <= ' ') {
              c = read();
          }
          boolean neg = (c == '-');
          if (neg)
              c = read();
          do {
              ret = ret * 10 + c - '0';
          } while ((c = read()) >= '0' && c <= '9');
  
          if (neg)
              return -ret;
          return ret;
      }
  
      public long nextLong() throws IOException {
          long ret = 0;
          byte c = read();
          while (c <= ' ')
              c = read();
          boolean neg = (c == '-');
          if (neg)
              c = read();
          do {
              ret = ret * 10 + c - '0';
          } while ((c = read()) >= '0' && c <= '9');
          if (neg)
              return -ret;
          return ret;
      }
  
      public double nextDouble() throws IOException {
          double ret = 0, div = 1;
          byte c = read();
          while (c <= ' ')
              c = read();
          boolean neg = (c == '-');
          if (neg)
              c = read();
  
          do {
              ret = ret * 10 + c - '0';
          } while ((c = read()) >= '0' && c <= '9');
  
          if (c == '.') {
              while ((c = read()) >= '0' && c <= '9') {
                  ret += (c - '0') / (div *= 10);
              }
          }
  
          if (neg)
              return -ret;
          return ret;
      }
  
      private void fillBuffer() throws IOException {
          bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
          if (bytesRead == -1)
              buffer[0] = -1;
      }
  
      private byte read() throws IOException {
          if (bufferPointer == bytesRead)
              fillBuffer();
          return buffer[bufferPointer++];
      }
  
      public void close() throws IOException {
          if (din == null)
              return;
          din.close();
      }
  }
   
   