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 whatever //do not write package name here */

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

public class GFG {
    
	public static void main (String[] args)throws IOException {
	     BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
 
        int t=Integer.parseInt(br.readLine());
       
        while(t-->0)
        {
           
            int n = Integer.parseInt(br.readLine());
            String str[] = br.readLine().split(" ");
            long a[] = new long[n];
            long sum = 0;
            for(int i=0;i<n;i++)
            {
                a[i]=Long.parseLong(str[i]);
                sum+=a[i];
            }
            
            long k= ((long)n*n+n)/2;
            boolean flag = true;
            
            if(sum%k==0)
            {
                long id = sum/k;
                long b[] = new long[n];
                if((id-a[0]+a[n-1])%n!=0  && (id-a[0]+a[n-1])>0)
                flag = false;
                b[0]=Math.abs((id-a[0]+a[n-1])/n);
                for(int i=1;i<n;i++)
                {
                    if((id-a[i]+a[i-1])%n!=0 && (id-a[i]+a[i-1])>0)
                    flag = false;
                   
                    b[i]=Math.abs((id-a[i]+a[i-1])/n);
                    
                }
                
                for(int i=0;i<n;i++)
                {
                    if(b[i]==0)
                    flag=false;
                }
                 
                
               
                
                if(flag)
                {
                    System.out.println("YES");
                    for(int i=0;i<n;i++)
                    System.out.print(b[i]+" ");
                    
                    System.out.println();
                }
                else
                {
                    System.out.println("NO");
                }
                
            }
            else
            {
                System.out.println("NO");
            }
          
        }
	}
}