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. 
// 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];
    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;
    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;
      }
      a[i] = (int) (diff / n);
    }
    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);
    }
  }
}
