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 q5 {
      public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  //    public static long mod = 1000000007;
  
      public static void solve() throws Exception {
          String[] parts = br.readLine().split(" ");
          long n = Integer.parseInt(parts[0]);
  
          long[] arr = new long[(int)n];
  
          long sum = 0;
          parts = br.readLine().split(" ");
          for (int i = 0; i < n; i++) {
              arr[i] = Integer.parseInt(parts[i]);
              sum += arr[i];
          }
  
          if(n == 1){
              System.out.println("YES");
              System.out.println(arr[0]);
              return;
          }
          if(n == 2){
              long a = -arr[0] + 2 * arr[1];
              long b = 2 * arr[0] - arr[1];
  
              if(a <= 0 || b <= 0 || a % 3 != 0 || b % 3 != 0) System.out.println("NO");
              else{
                  System.out.println("YES");
                  System.out.println((a / 3) + " " + (b / 3));
              }
              return;
          }
  
          long det = (n * n * (n + 1)) / 2;
  
          long v1 = (n * (n + 1)) / 2 + 1;
          long v2 = 2 - v1;
  
          int idx1 = 0,idx2 = (int)n - 1;
          StringBuilder ans = new StringBuilder();
          for(int i = 0;i < n;i++){
              long val = sum - arr[idx1] - arr[idx2];
              val += arr[idx1]  * v2;
              val += arr[idx2] * v1;
  
              idx1  = (idx1 + 1) % (int)n;
              idx2  = (idx2 + 1) % (int)n;
  
              if(val <= 0 || val % det != 0){
                  System.out.println("NO");
                  return;
              }
  
              ans.append(val / det).append(" ");
          }
          System.out.println("YES");
          System.out.println(ans);
      }
  
      public static void main(String[] args) throws Exception {
          int tests = Integer.parseInt(br.readLine());
          for (int test = 1; test <= tests; test++) {
              solve();
          }
      }
  
  //    public static void sort(int[] arr){
  //        ArrayList<Integer> temp = new ArrayList<>();
  //        for(int val : arr) temp.add(val);
  //
  //        Collections.sort(temp);
  //
  //        for(int i = 0;i < arr.length;i++) arr[i] = temp.get(i);
  //    }
  //    public static void sort(long[] arr){
  //        ArrayList<Long> temp = new ArrayList<>();
  //        for(long val : arr) temp.add(val);
  //
  //        Collections.sort(temp);
  //
  //        for(int i = 0;i < arr.length;i++) arr[i] = temp.get(i);
  //    }
  //
  //    public static long power(long a,long b,long mod){
  //        if(b == 0) return 1;
  //
  //        long p = power(a,b / 2,mod);
  //        p = (p * p) % mod;
  //
  //        if(b % 2 == 1) return (p * a) % mod;
  //        return p;
  //    }
  //
  //    public static int GCD(int a,int b){
  //        return b == 0 ? a : GCD(b,a % b);
  //    }
  //    public static long GCD(long a,long b){
  //        return b == 0 ? a : GCD(b,a % b);
  //    }
  //
  //    public static int LCM(int a,int b){
  //        return a * b / GCD(a,b);
  //    }
  //    public static long LCM(long a,long b){
  //        return a * b / GCD(a,b);
  //    }
  }
  