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 Main {
   // For fast input output
   static class FastReader {
       BufferedReader br;
       StringTokenizer st;
       public FastReader()
       { try {br = new BufferedReader(
       new FileReader("input.txt"));
       PrintStream out = new PrintStream(new FileOutputStream("output.txt"));
       System.setOut(out);}
       catch(Exception e) { br = new BufferedReader(new InputStreamReader(System.in));}
       }
       String next()
       {
       while (st == null || !st.hasMoreElements()) {
                   try {st = new StringTokenizer(br.readLine());}
                   catch (IOException e) {
                   e.printStackTrace();}
               }
               return st.nextToken();
       }
       int nextInt() { return Integer.parseInt(next()); }
       long nextLong() { return Long.parseLong(next()); }
       double nextDouble() {return Double.parseDouble(next()); }
       String nextLine()
       {
           String str = "";
           try {
           str = br.readLine();
           }
           catch (IOException e) {
               e.printStackTrace();
           }
           return str;
       }
   }
    // end of fast i/o code
    public static void main(String[] args) {
        FastReader reader = new FastReader();
        StringBuilder sb = new StringBuilder("");
        
        int t = reader.nextInt();
        while(t-->0){
            int n = reader.nextInt();
            
            int arr[] = new int[n];
            int ans[] = new int[n];
            boolean possible = true;
            int sum = 0;
            for(int i=0; i<n; i++){
                arr[i] = reader.nextInt();
                sum += arr[i];
            }

            if(n==1){
                sb.append("YES\n");
                sb.append(arr[0]+"\n");
                continue;
            }

            int t1 = (n*(n+1))/2;
            if(sum%t1!=0){
                possible = false;
                sb.append("NO\n");
                continue;
            }

            t1 = sum/t1;
            // sb.append(t+" "+t1);
            for(int i=0; i<n; i++){
                int j = i-1;
                if(i==0){
                    j = n-1;
                }
                ans[i] = arr[j] - (arr[i]-t1);
                // sb.append(t+" "+ans[i]+" "+i+" \n");
                if(ans[i]<=0){
                    possible = false;
                    break;
                }
                if(ans[i]%n!=0){
                    possible = false;
                    break;
                }
                ans[i] /= n;
            }

            if(!possible){
                sb.append("NO\n");
            }else{
                sb.append("YES\n");
                for(int i=0; i<n; i++){
                    sb.append(ans[i]+" ");
                }
                sb.append("\n");
            }
        }
        System.out.println(sb);
    }
}