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. 
import java.util.*;
import java.io.*;

public class Solution {
    
    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int t = Integer.parseInt(br.readLine());

        BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));

        StringTokenizer st;

        while (t-- > 0) {

            int n = Integer.parseInt(br.readLine());

            st = new StringTokenizer(br.readLine());

            int arr[] = new int[n];
            long arr2[] = new long[n];

            long sumb = 0;
            for(int i = 0; i < n; i++)
            {
            int e = Integer.parseInt(st.nextToken());
            arr[i] = e;
            sumb+=e;
            }

            long suma = 0;
            long nt = n * (n+1);
            nt/=2;

            if(sumb % nt != 0)
            {
                output.write("NO\n");
                continue;
            }

            suma = sumb / nt;

            int flag = 0;
            
            for(int i = 0; i < n; i++)
            {
                if(i == n - 1)
                {
                    long diff = arr[i] - arr[0] + suma;
                    if(diff % n != 0 || diff <= 0)
                    flag = 1;
                    arr2[0] = diff / n;
                    continue;
                }
                long diff = arr[i] - arr[i+1] + suma;
                if(diff % n != 0 || diff <= 0)
                    flag = 1;
                
                arr2[i+1] = diff / n;
            }

            if(flag == 1)
            {
                output.write("NO\n");
                continue;
            }

            output.write("YES\n");
            for(long i : arr2)
                output.write(i + " ");

            output.write("\n");




            // int k = Integer.parseInt(st.nextToken());

            // char arr[] = br.readLine().toCharArray();

            // output.write();
            // int n = Integer.parseInt(st.nextToken());

            // HashMap<Character, Integer> map = new HashMap<Character, Integer>();

            // if
            // output.write("YES\n");
            // else
            // output.write("NO\n");

            // long a = Long.parseLong(st.nextToken());
            // long b = Long.parseLong(st.nextToken());

            // if(flag == 1)
            // output.write("NO\n");
            // else
            // output.write("YES\n" + x + " " + y + " " + z + "\n");

            // output.write(n+ "\n");

        }

        output.flush();

    }

}