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 Solution {
      static int M = 998244353; //1_000_000_007;
      static Random rng = new Random();
  
      private static int[] testCase(int n, int[] b) {
          int[] ans = new int[n];
          long sum = 0, s, na;
  
          for (int bi : b) {
              sum += bi;
          }
  
          if (sum % ((n * (n + 1)) >> 1) == 0) {
              s = sum / ((n * (n + 1)) >> 1);
  
              for (int i = 0; i < n; i++) {
                  na = (i == 0 ? b[n - 1] : b[i - 1]) - (b[i] - s);
  
                  if (na % n != 0) {
                      return null;
                  }
  
                  ans[i] = (int) (na / n);
                  
                  if (ans[i] <= 0) {
                      return null;
                  }
              }
  
              return ans;
          } else {
              return null;
          }
      }
  
      public static void main(String[] args) {
          FastScanner in = new FastScanner();
          PrintWriter out = new PrintWriter(System.out);
          int t = in.nextInt();  // Scanner has functions to read ints, longs, strings, chars, etc.
          //in.nextLine();
          for (int tt = 1; tt <= t; ++tt) {
              int n = in.nextInt();
              int[] b = in.readArray(n);
  
              int[] ans = testCase(n, b);
  
              if (ans == null) {
                  out.println("NO");
              } else {
                  out.println("YES");
  
                  for (int an : ans) {
                      out.print(an + " ");
                  }
  
                  out.println();
              }
          }
  
          out.close();
      }
  
      private static class FastScanner {
          BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
          StringTokenizer st = new StringTokenizer("");
          String next() {
              while (!st.hasMoreTokens())
                  try {
                      st = new StringTokenizer(br.readLine());
                  } catch (IOException e) {
                      e.printStackTrace();
                  }
              return st.nextToken();
          }
  
          boolean hasNext() {
              return st.hasMoreTokens();
          }
  
          char[] readCharArray(int n) {
              char[] arr = new char[n];
              try {
                  br.read(arr);
                  br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return arr;
          }
  
          int nextInt() {
              return Integer.parseInt(next());
          }
  
          int[] readArray(int n) {
              int[] a = new int[n];
              for (int i = 0; i < n; i++) a[i] = nextInt();
              return a;
          }
  
          long[] readLongArray(int n) {
              long[] a = new long[n];
              for (int i = 0; i < n; i++) a[i] = nextLong();
              return a;
          }
  
          long nextLong() {
              return Long.parseLong(next());
          }
      }
  
      private static void sort(int[] arr) {
          int temp, idx;
  
          for (int i = arr.length - 1; i > 0; i--) {
              idx = rng.nextInt(i + 1);
  
              temp = arr[i];
              arr[i] = arr[idx];
              arr[idx] = temp;
          }
  
          Arrays.sort(arr);
      }
  
      private static void sort(long[] arr) {
          long temp;
          int idx;
  
          for (int i = arr.length - 1; i > 0; i--) {
              idx = rng.nextInt(i + 1);
  
              temp = arr[i];
              arr[i] = arr[idx];
              arr[idx] = temp;
          }
  
          Arrays.sort(arr);
      }
  
      private static <T> void sort(T[] arr) {
          T temp;
          int idx;
  
          for (int i = arr.length - 1; i > 0; i--) {
              idx = rng.nextInt(i + 1);
  
              temp = arr[i];
              arr[i] = arr[idx];
              arr[idx] = temp;
          }
  
          Arrays.sort(arr);
      }
  
      private static <T> void sort(T[] arr, Comparator<? super T> cmp) {
          T temp;
          int idx;
  
          for (int i = arr.length - 1; i > 0; i--) {
              idx = rng.nextInt(i + 1);
  
              temp = arr[i];
              arr[i] = arr[idx];
              arr[idx] = temp;
          }
  
          Arrays.sort(arr, cmp);
      }
  
      private static <T extends Comparable<? super T>> void sort(List<T> list) {
          T temp;
          int idx;
  
          for (int i = list.size() - 1; i > 0; i--) {
              idx = rng.nextInt(i + 1);
  
              temp = list.get(i);
              list.set(i, list.get(idx));
              list.set(idx, temp);
          }
  
          Collections.sort(list);
      }
  
      private static <T> void sort(List<T> list, Comparator<? super T> cmp) {
          T temp;
          int idx;
  
          for (int i = list.size() - 1; i > 0; i--) {
              idx = rng.nextInt(i + 1);
  
              temp = list.get(i);
              list.set(i, list.get(idx));
              list.set(idx, temp);
          }
  
          Collections.sort(list, cmp);
      }
  
      class DSU {
          int[] parent, rank;
  
          public DSU(int n) {
              parent = new int[n];
              rank = new int[n];
  
              for (int i = 0; i < n; i++) {
                  parent[i] = i;
              }
          }
  
          public int find(int i) {
              if (parent[i] == i) {
                  return i;
              } else {
                  int res = find(parent[i]);
                  parent[i] = res;
  
                  return res;
              }
          }
  
          public boolean isSameSet(int i, int j) {
              return find(i) == find(j);
          }
  
          public void union(int i, int j) {
              int iParent = find(i), jParent = find(j);
  
              if (iParent != jParent) {
                  if (rank[iParent] > rank[jParent]) {
                      parent[jParent] = iParent;
                  } else {
                      parent[iParent] = jParent;
  
                      if (rank[iParent] == rank[jParent]) {
                          rank[jParent]++;
                      }
                  }
              }
          }
      }
  }