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.BufferedReader;
  import java.io.BufferedWriter;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.io.OutputStreamWriter;
  import java.lang.reflect.Array;
  import java.util.*;
  import java.util.stream.Stream;
  
  public class Program {
  
      static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
      static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
  
      public static void main(String[] args) throws NumberFormatException, IOException {
  
          int cases = Integer.parseInt(reader.readLine());
          int mod = 998244353;
  
          while(cases-- > 0) {
  
              String[] firstLine = reader.readLine().split(" ");
              int n = Integer.parseInt(firstLine[0]);
              //int k = Integer.parseInt(firstLine[1]);
              long[] arr = convertToLongPrimitiveArray(reader.readLine().split(" "));
  
              long sum = (Arrays.stream(arr).sum());
  
              long deno = ((long)n*((long)n+1))/2;
  
              if(sum%deno != 0) {
                  printNo();
                  continue;
              }
  
              sum /= deno;
              long[] ans = new long[n];
              boolean pos = true;
  
              for(int i=1;i<=n;i++) {
                  long a = arr[(i-1)%n];
                  long b = arr[i%n];
                  long diff = b-a;
                  if((sum-diff)%n != 0) {
                      pos = false;
                      break;
                  }
                  ans[i%n] = (sum-diff)/n;
  
                  if(ans[i%n] <= 0) {
                      pos = false;
                      break;
                  }
              }
  
              if(!pos) {
                  printNo();
                  continue;
              }
  
              printYes();
  
              for(int i=0;i<n;i++) {
                  out.append(ans[i] + " ");
              }
  
              out.append("\n");
  
          }
  
          out.flush();
  
      }
  
      public static int[] convertToIntPrimitiveArray(String[] str) {
          return Stream.of(str).mapToInt(Integer::parseInt).toArray();
      }
  
      public static Integer[] convertToIntArray(String[] str) {
          Integer[] arr = new Integer[str.length];
          for(int i=0;i<str.length;i++) {
              arr[i] = Integer.parseInt(str[i]);
          }
          return arr;
      }
  
      public static Long[] convertToLongArray(String[] str) {
          Long[] arr = new Long[str.length];
          for(int i=0;i<str.length;i++) {
              arr[i] = Long.parseLong(str[i]);
          }
          return arr;
      }
  
      public static long[] convertToLongPrimitiveArray(String[] str) {
          return Stream.of(str).mapToLong(Long::parseLong).toArray();
      }
  
      public static void printYes() throws IOException {
          out.append("YES" + "\n");
      }
  
      public static void printNo() throws IOException {
          out.append("NO" + "\n");
      }
  
      public static void printNumber(long num) throws IOException {
          out.append(num + "\n");
      }
  
      public static long hcf(long a, long b) {
          if(b==0) return a;
          return hcf(b, a%b);
      }
  
      public static int findSet(int[] parent, int[] rank, int v) {
          if(v==parent[v]) {
              return v;
          }
          parent[v] = findSet(parent, rank, parent[v]);
          return parent[v];
      }
  
      public static void unionSet(int[] parent, int[] rank, int a, int b) {
  
          a = findSet(parent, rank, a);
          b = findSet(parent, rank, b);
  
          if(a == b) {
              return;
          }
  
          if(rank[a] < rank[b]) {
              int temp = a;
              a = b;
              b = temp;
          }
  
          parent[b] = a;
          if(rank[a] == rank[b]) {
              rank[a]++;
          }
  
      }
  
      public static void makeSet(int[] parent, int[] rank, int v) {
          parent[v] = v;
          rank[v] = 0;
      }
  
      public static long modularDivision(long a, long b, int mod) {
          if(a==0) return 1;
          a %= mod;
          long res = 1L;
          while(b > 0) {
              if((b&1)==1) {
                  res = (res * a)%mod;
              }
              a = (a*a)%mod;
              b >>= 1;
          }
          return res;
      }
  
      public static void customSort(int[] arr) {
          int n = arr.length;
          Random rnd = new Random();
          for(int i=0; i<n; ++i){
              int tmp = arr[i];
              int randomPos = i + rnd.nextInt(n-i);
              arr[i] = arr[randomPos];
              arr[randomPos] = tmp;
          }
          Arrays.sort(arr);
          return;
      }
  
      public static long[] factorial(int n, int mod) {
          long[] fact = new long[n+1];
          fact[0] = 1;
          for(int i=1;i<fact.length;i++) {
              fact[i] = (i*fact[i-1] + mod)%mod;
          }
          return fact;
      }
  
  }