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.lang.*;
 import java.io.*;

public class E_Singers_Tour
 {
     static int M = 1_000_000_007;
     static final PrintWriter out =new PrintWriter(System.out);
     static final FastReader fs = new FastReader();
     static boolean prime[];
     public static void main (String[] args) throws java.lang.Exception
     {
           
           int t= fs.nextInt();
          aaa: for(int i=0;i<t;i++)
           {
               int n= fs.nextInt();
               long a[]=fs.arrayIn(n);
               long sum=0;
               long sumn=(long)n*(long)(n+1);
               sumn=sumn/2;
               for(int j=0;j<n;j++){
                   sum+=(long)a[j];
               }
               if(sum%sumn!=0){
                   out.println("NO");
                   continue aaa;
               }
               long suma=sum/sumn;
               int ans[]=new int[n];
               for(int j=1;j<n;j++){
                   long kl=(long)a[j-1]-(long)a[j]+suma;
                   if(kl<=0||kl%(long)n!=0){
                    out.println("NO");
                    continue aaa;
                   }
                   ans[j]=(int)(kl/(long)n);
               }
               long kl=(long)a[n-1]-(long)a[0]+suma;
                   if(kl<=0||kl%(long)n!=0){
                    out.println("NO");
                    continue aaa;
                   }
                   ans[0]=(int)(kl/(long)n);
                   out.println("YES");
                   for(int j=0;j<n;j++){
                       out.print(ans[j]+" ");
                   }
                   out.println();
           }
           out.flush();
  }
  public static long power(long x, long y)
  {
      long temp;
      if (y == 0)
          return 1;
      temp = power(x, y / 2);

      if (y % 2 == 0)
          return modMult(temp,temp);
      else {
          if (y > 0)
              return modMult(x,modMult(temp,temp));
          else
              return (modMult(temp,temp)) / x;
      }
  }
  static void sieveOfEratosthenes(int n)
    {
         prime = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
            prime[i] = true;
            prime[0]=false;
            if(1<=n)
            prime[1]=false;
        for (int p = 2; p * p <= n; p++)
        {
            
            if (prime[p] == true)
            {
               
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }
         static class FastReader 
         {
         BufferedReader br;
         StringTokenizer st;
  
         public FastReader()
         {
             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;
         }
 long [] arrayIn(int n) throws IOException
     {
         long  arr[] = new long[n];
         for(int i=0; i<n; i++)
         {
             arr[i] = nextLong();
         }
         return arr;
     }
     }
     
     public static class Pairs implements Comparable<Pairs>
     {
         int value,index;
         Pairs(int value, int index)
         {
             this.value = value;
             this.index = index;
         }
         public int compareTo(Pairs p)
         {
             return Integer.compare(this.value, p.value);
         }
     }
     static final Random random = new Random();
  
     static void ruffleSort(int arr[])
     {
         int n = arr.length;
         for(int i=0; i<n; i++)
         {
             int j = random.nextInt(n),temp = arr[j];
             arr[j] = arr[i];
             arr[i] = temp;
         }
         Arrays.sort(arr);
     }
     static long nCk(int n, int k) {
         return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
     }
  
     static long fact (long n) {
  
         long fact =1;
         for(int i=1; i<=n; i++) {
             fact = modMult(fact,i);
         }
         return fact%M;
     }
  
     static long modMult(long a,long b) {
         return a*b%M;
     }
  
     static long fastexp(long x, int y){
         if(y==1) return x;
  
         long ans = fastexp(x,y/2);
         if(y%2 == 0) return modMult(ans,ans);
         else return modMult(ans,modMult(ans,x));
     }
 }