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.Arrays;
  import java.util.Locale;
  import java.util.StringTokenizer;
  
  public class E {
  
      private final boolean MULTI_TEST = true;
      private final String FILE_NAME = "";
  
      private void solve() {
          int n = ri();
          long[] b = new long[n];
          long sumB = 0;
          for(int i = 0; i < n; i++) {
              b[i] = rl();
              sumB+=b[i];
          }
          boolean flag = true;
          long sumA = 2 * sumB / ((long) n * (n + 1));
          if(sumA * n * (n+1) != 2*sumB) flag = false;
          long[] a = new long[n];
          for (int i = 1; i < n; i++) {
              a[i] = (b[i-1] - b[i] + sumA)/n;
              if (a[i] <= 0) {
                  flag = false;
                  break;
              }
          }
  
          a[0] = (b[n-1] - b[0] + sumA)/n; //if n == 1, then a[0] = sumA/n = sumA - true
          if(a[0] <= 0) flag = false;
          if(!flag || sum(a) != sumA) {
              out.println("NO");
          } else {
              out.println("YES");
              StringBuilder builder = new StringBuilder();
              for(long l : a) {
                  builder.append(l).append(" ");
              }
              out.println(builder);
          }
      }
  
      //////////////////////////////////////////////////////////////////
  
      long sqrtLong(long x) {
          long root = (long) Math.sqrt(x);
          while (root * root > x) --root;
          while ((root + 1) * (root + 1) <= x) ++root;
          return root;
      }
  
      int gcd(int a, int b) {
          if (b == 0)
              return a;
          else
              return gcd(b, a % b);
      }
  
      int lcm(int a, int b) {
          return a / gcd(a, b) * b;
      }
  
      int phi(int n) {
          int result = n;
          for (int i = 2; i * i <= n; ++i)
              if (n % i == 0) {
                  while (n % i == 0)
                      n /= i;
                  result -= result / i;
              }
          if (n > 1)
              result -= result / n;
          return result;
      }
  
      int factmod(int n, int p) {
          int res = 1;
          while (n > 1) {
              res = (res * ((n / p) % 2 == 1 ? p - 1 : 1)) % p;
              for (int i = 2; i <= n % p; ++i)
                  res = (res * i) % p;
              n /= p;
          }
          return res % p;
      }
  
      int binpow(int a, int n) {
          int res = 1;
          while (n != 0) {
              if ((n & 1) != 0)
                  res *= a;
              a *= a;
              n >>= 1;
          }
          return res;
      }
  
      String solPyatnashki() {
          int a[] = new int[16];
          for (int i = 0; i < 16; ++i)
              a[i] = ri();
  
          int inv = 0;
          for (int i = 0; i < 16; ++i)
              if (a[i] != 0)
                  for (int j = 0; j < i; ++j)
                      if (a[j] > a[i])
                          ++inv;
          for (int i = 0; i < 16; ++i)
              if (a[i] == 0)
                  inv += 1 + i / 4;
  
  
          return ((inv & 1) != 0 ? "No Solution" : "Solution Exists");
      }
  
      boolean isPrime(int number) {
          for (int i = 2; i * i <= number; i++) {
              if (number % i == 0) {
                  return false;
              }
          }
          return number > 1;
      }
  
      boolean[] primes(int border) {
          boolean[] isPrimes = new boolean[border + 1];
          Arrays.fill(isPrimes, true);
          isPrimes[0] = false;
          isPrimes[1] = false;
          for (int i = 2; i < border + 1; i++) {
              if (!isPrimes[i]) continue;
              for (int k = i * 2; k < border; k += i) {
                  isPrimes[k] = false;
              }
          }
          return isPrimes;
      }
  
      int[] sort(int[] arr) {
          Integer[] a = new Integer[arr.length];
          for (int i = 0; i < arr.length; i++) {
              a[i] = arr[i];
          }
          Arrays.sort(a);
          for (int i = 0; i < a.length; i++) {
              arr[i] = a[i];
          }
          return arr;
      }
  
      long[] sort(long[] arr) {
          Long[] a = new Long[arr.length];
          for (int i = 0; i < arr.length; i++) {
              a[i] = arr[i];
          }
          Arrays.sort(a);
          for (int i = 0; i < a.length; i++) {
              arr[i] = a[i];
          }
          return arr;
      }
  
      int max(int[] a) {
          int max = Integer.MIN_VALUE;
          for (int i = 0; i < a.length; i++) {
              if (a[i] > max) max = a[i];
          }
          return max;
      }
  
      long max(long[] a) {
          long max = Long.MIN_VALUE;
          for (int i = 0; i < a.length; i++) {
              if (a[i] > max) max = a[i];
          }
          return max;
      }
  
      int min(int[] a) {
          int min = Integer.MAX_VALUE;
          for (int i = 0; i < a.length; i++) {
              if (a[i] < min) min = a[i];
          }
          return min;
      }
  
      long min(long[] a) {
          long min = Long.MAX_VALUE;
          for (int i = 0; i < a.length; i++) {
              if (a[i] < min) min = a[i];
          }
          return min;
      }
  
      long sum(long[] a) {
          long s = 0;
          for (int i = 0; i < a.length; i++) {
              s += a[i];
          }
          return s;
      }
  
      long fastMod(String s1, long n2) {
          long num = 0;
          for (int i = 0; i < s1.length() - 1; i++) {
              num += Integer.parseInt(String.valueOf(s1.charAt(i)));
              num *= 10;
              if (num >= n2) {
                  num = num % n2;
              }
          }
          return (num + Integer.parseInt(String.valueOf(s1.charAt(s1.length() - 1)))) % n2;
      }
  
      //////////////////////////////////////////////////////////////////
  
      private boolean yesNo(boolean yes) {
          return yesNo(yes, "YES", "NO");
      }
  
      private boolean yesNo(boolean yes, String yesString, String noString) {
          out.println(yes ? yesString : noString);
          return yes;
      }
  
      //////////////////////////////////////////////////////////////////
  
      private long rl() {
          return Long.parseLong(rs());
      }
  
      private double rd() {
          return Double.parseDouble(rs());
      }
  
      private int[] ria(int n) {
          int[] a = new int[n];
          for (int i = 0; i < n; ++i) a[i] = ri();
          return a;
      }
  
      private int ri() {
          return Integer.parseInt(rs());
      }
  
      private String rs() {
          while (!tok.hasMoreTokens()) {
              String nextLine = readLine();
              if (null == nextLine) return null;
              tok = new StringTokenizer(nextLine);
          }
  
          return tok.nextToken();
      }
  
      private String readLine() {
          try {
              return in.readLine();
          } catch (IOException e) {
              throw new RuntimeException(e);
          }
      }
  
      //////////////////////////////////////////////////////////////////
  
      private BufferedReader in;
      private StringTokenizer tok;
      private PrintWriter out;
  
      private void initFileIO(String inputFileName, String outputFileName) throws FileNotFoundException {
          in = new BufferedReader(new FileReader(inputFileName));
          out = new PrintWriter(outputFileName);
      }
  
      private void initConsoleIO() throws IOException {
          in = new BufferedReader(new InputStreamReader(System.in));
          out = new PrintWriter(System.out);
      }
  
      private void initIO() throws IOException {
          Locale.setDefault(Locale.US);
  
          if (!FILE_NAME.isEmpty()) {
              initFileIO(FILE_NAME + ".in", FILE_NAME + ".out");
          } else {
              if (new File("input.txt").exists()) {
                  initFileIO("input.txt", "output.txt");
              } else {
                  initConsoleIO();
              }
          }
  
          tok = new StringTokenizer("");
      }
  
      //////////////////////////////////////////////////////////////////
  
      private void run() {
          try {
              long timeStart = System.currentTimeMillis();
              initIO();
              if (MULTI_TEST) {
                  int t = ri();
                  while (t-- > 0) {
                      solve();
                      out.flush();
                  }
              } else
                  solve();
              out.close();
              long timeEnd = System.currentTimeMillis();
              System.err.println("Time(ms) = " + (timeEnd - timeStart));
          } catch (Exception e) {
              e.printStackTrace();
              throw new RuntimeException(e);
          }
      }
  
      public static void main(String[] args) {
          new E().run();
      }
  
      ///////////////////////////////////////////////////////////////////
  }
  