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 c1618;
  
  import java.io.File;
  import java.lang.invoke.MethodHandles;
  import java.util.Random;
  import java.util.Scanner;
  
  //
  // Codeforces Round #760 (Div. 3) 2021-12-14 06:35
  // E. Singers' Tour
  // https://codeforces.com/contest/1618/problem/E
  // time limit per test 2 seconds; memory limit per test 256 megabytes
  // public class Pseudo for 'Source should satisfy regex [^{}]*public\s+(final)?\s*class\s+(\w+).*'
  //
  // 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 \in [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 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 . Otherwise, on the first line print , 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.
  //
  public class C1618E {
    static final int MOD = (int)1e9+7;
    static final Random RAND = new Random();
  
    static int[] solve(int[] b) {
      int n = b.length;
      int[] a = new int[n];
  
      // Example of test case 4: n = 6:
      //   1  6  5  4  3  2  -> 81
      //   2  1  6  5  4  3  -> 75
      //   3  2  1  6  5  4  -> 75
      //   4  3  2  1  6  5  -> 93
      //   5  4  3  2  1  6  -> 93
      //   6  5  4  3  2  1  -> 87
      // Add all together we have 21 * s = 504 -> s = 24
      long sum = 0;
      for (int v : b) {
        sum += v;
      }
      int m = n * (n + 1) / 2;
      if (sum % m != 0) {
        return null;
      }
      long s = sum / m;
      // previous row + s - current row:
      //   6  0  0  0  0  0  ->  30  -> a[0] = 5
      //   0  6  0  0  0  0  ->  30  -> a[1] = 5
      //   ...
      for (int i = 0; i < n; i++) {
        long diff = s + b[(i+n-1) % n] - b[i];
        if (diff == 0 || diff % n != 0) {
          return null;
        }
        diff /= n;
        if (diff <= 0 || diff > 1000000000) {
          return null;
        }
        a[i] = (int) diff;
      }
      return a;
    }
  
    public static void main(String[] args) {
      Scanner in = getInputScanner();
      int T = in.nextInt();
      for (int t = 1; t <= T; t++) {
        int n = in.nextInt();
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
          b[i] = in.nextInt();
        }
        int[] ans = solve(b);
        if (ans == null) {
          System.out.println("NO");
        } else {
          System.out.println("YES");
          StringBuilder sb = new StringBuilder();
          for (int v : ans) {
            sb.append(v);
            sb.append(' ');
          }
          System.out.println(sb.toString().trim());
        }
      }
      in.close();
    }
  
    static Scanner getInputScanner() {
      try {
        final String USERDIR = System.getProperty("user.dir");
        final String CNAME = MethodHandles.lookup().lookupClass().getSimpleName();
        final File fin = new File(USERDIR + "/io/c" + CNAME.substring(1,5) + "/" + CNAME + ".in");
        return fin.exists() ? new Scanner(fin) : new Scanner(System.in);
      } catch (Exception e) {
        return new Scanner(System.in);
      }
    }
  }
  