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. 
// Don't place your source in a package


import javax.swing.*;
import java.lang.reflect.Array;
import java.text.DecimalFormat;
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
import java.util.stream.Stream;



// Please name your class Main
public class Main {
    static FastScanner fs=new FastScanner();
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next() {
            while (!st.hasMoreElements())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        int Int() {
            return Integer.parseInt(next());
        }

        long Long() {
            return Long.parseLong(next());
        }

        String Str(){
            return next();
        }
    }


    public static void main (String[] args) throws java.lang.Exception {
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        //reading /writing file
        //Scanner in=new Scanner(System.in);
        //Scanner in=new Scanner(new File("input.txt"));
        //PrintWriter pr=new PrintWriter("output.txt");


        int T=Int();
        for(int t=0;t<T;t++){
            Solution sol1=new Solution(out,fs);
            sol1.solution(t);
        }
        out.flush();

    }


    public static int[] Arr(int n){
        int A[]=new int[n];
        for(int i=0;i<n;i++)A[i]=Int();
        return A;
    }
    public static int Int(){
        return fs.Int();
    }
    public static long Long(){
        return fs.Long();
    }
    public static String Str(){
        return fs.Str();
    }

}








class Solution {
    PrintWriter out;
    int INF = Integer.MAX_VALUE;
    int NINF = Integer.MIN_VALUE;
    int MOD = 998244353;
    int mod = 1000000007;
    Main.FastScanner fs;

    //int mu[];
    //int musum[];

    public Solution(PrintWriter out,Main.FastScanner fs) {
        this.out = out;
        this.fs=fs;
        //muinit(100000);
    }


    /*public void muinit(int n){
        int N = n + 10;
        mu = new int[N];
        musum = new int[N];
        mu[1] = 1;


        boolean seen[] = new boolean[N];
        int primes[] = new int[N];
        int cnt = 0;

        for (int i = 2; i < mu.length; i ++ ) {
            if (!seen[i]) {
                primes[cnt++] = i;
                mu[i] = -1;
            }
            for (int j = 0; primes[j] * i < N; j ++ ) {
                seen[primes[j] * i] = true;
                if (i % primes[j] == 0) break;
                mu[primes[j] * i] = -mu[i];
            }
        }

        for (int i = 1; i < N; i ++ ){
            musum[i] = musum[i - 1] + mu[i];
        }
    }*/




    public void solution(int testcase) {
        int n = fs.Int();
        long B[]=new long[n];
        long sum = 0;
        for(int i = 0; i < n; i++){
            B[i]=fs.Int();
            sum += B[i];
        }
        long res[] = new long[n];
        if((sum % ((1l + n) * n / 2)) != 0){
            out.println("NO");
            return;
        }

        long avg = (sum / ((1l + n) * n / 2));

        for(int i = 0; i < n; i++){
            int j = (i + 1) % n;
            long dif = B[j] - B[i];
            dif -= avg;
            if(Math.abs(dif) % n != 0){
                out.println("NO");
                return;
            }
            res[j] = -(dif / n);
            if(res[j] < 1) {
                out.println("NO");
                return; 
            }
        }


        out.println("YES");
        for(long i:res){
            out.print(i+" ");
        }out.println();
    }

}

