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: //package Codeforces.Round760Div3;
  
  import java.io.*;
  import java.util.*;
  
  public class E {
      public static void main(String[] args) throws IOException {
          Soumit sc = new Soumit();
  
          int t = sc.nextInt();
          StringBuilder sb = new StringBuilder();
          while (t-->0){
              int n = sc.nextInt();
              long[] b = sc.nextLongArray(n);
  
              long sumOfNatural = (n * ((long) n + 1))/2;
              long sum = 0;
              for(long i: b)
                  sum += i;
  
              if(sum%sumOfNatural!=0){
                  sb.append("NO\n");
                  continue;
              }
              sum = sum / sumOfNatural;
  
              long[] a = new long[n];
              boolean flag = true;
              for(int i=0;i<n;i++){
                  a[i] = sum + b[(i-1 + n)%n] - b[i];
                  if(a[i]%n!=0 || a[i]<=0){
                      flag = false;
                      break;
                  }
  
                  a[i] = a[i] / n;
              }
  
              if(flag){
                  sb.append("YES\n");
                  for(int i=0;i<n;i++){
                      sb.append(a[i]).append(" ");
                  }
                  sb.append("\n");
              }
              else{
                  sb.append("NO\n");
              }
          }
  
          System.out.println(sb);
  
          sc.close();
      }
  
      static class Soumit {
          final private int BUFFER_SIZE = 1 << 18;
          final private DataInputStream din;
          final private byte[] buffer;
          private PrintWriter pw;
          private int bufferPointer, bytesRead;
          StringTokenizer st;
  
          public Soumit() {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public Soumit(String file_name) throws IOException {
              din = new DataInputStream(new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public void streamOutput(String file) throws IOException {
              FileWriter fw = new FileWriter(file);
              BufferedWriter bw = new BufferedWriter(fw);
              pw = new PrintWriter(bw);
          }
  
          public void println(String a) {
              pw.println(a);
          }
  
          public void print(String a) {
              pw.print(a);
          }
  
          public String readLine() throws IOException {
              byte[] buf = new byte[3000064]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n')
                      break;
                  buf[cnt++] = (byte) c;
              }
              return new String(buf, 0, cnt);
          }
  
          String next() {
              while (st == null || !st.hasMoreElements()) {
                  try {
                      st = new StringTokenizer(readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              }
              return st.nextToken();
          }
  
          public void sort(int[] arr) {
              ArrayList<Integer> arlist = new ArrayList<>();
              for (int i : arr)
                  arlist.add(i);
  
              Collections.sort(arlist);
              for (int i = 0; i < arr.length; i++)
                  arr[i] = arlist.get(i);
          }
  
          public void sort(long[] arr) {
              ArrayList<Long> arlist = new ArrayList<>();
              for (long i : arr)
                  arlist.add(i);
  
              Collections.sort(arlist);
              for (int i = 0; i < arr.length; i++)
                  arr[i] = arlist.get(i);
          }
  
          public int[] nextIntArray(int n) throws IOException {
              int[] arr = new int[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextInt();
              }
  
              return arr;
          }
  
          public long[] nextLongArray(int n) throws IOException {
              long[] arr = new long[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextLong();
              }
  
              return arr;
          }
  
          public double[] nextDoubleArray(int n) throws IOException {
              double[] arr = new double[n];
              for (int i = 0; i < n; i++) {
                  arr[i] = nextDouble();
              }
  
              return arr;
          }
  
          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;*/
              if (din != null) din.close();
              if (pw != null) pw.close();
          }
      }
  }
  