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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.TreeSet;
import java.util.TreeMap;
import java.util.PriorityQueue;
import java.util.Collections;

import java.util.LinkedList;
import java.util.Iterator;

public class First {

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int T = fs.nextInt();
        for (int tt = 0; tt < T; tt++) {

            solve(fs);
        }
        
    }
    static void solve(FastScanner fs)
    {
        int n=fs.nextInt();
        long[] arr=takeLong(n, fs);

        long sum=0;
        for(int i=0;i<n;++i)
            sum+=(arr[i]);

        long total=((long)n*(n+1)/2);

        if(sum%total!=0)
        {
            pn("NO"); return;
        }

        long s=sum/total;

        ArrayList<Long> ls=new ArrayList<>();

        for(int i=1;i<n;++i)
        {
            ls.add(arr[i]-arr[i-1]);
        }
        ls.add(arr[0]-arr[n-1]);

        long[] temp=new long[n];

        for(int i=1;i<=n;++i)
        {
            int idx=i%n;

            temp[idx]=s-ls.get(i-1);

            if(temp[idx]%n!=0)
            {
                pn("NO"); return;
            }

            temp[idx]/=n;
            if(temp[idx]<=0)
            {
                pn("NO"); return;
            }
        }
        pn("YES");
        for(long ele: temp)
            p(ele+" ");
        pn("");
    }
    static int MOD=(int)(1e9+7);
    
    static long gcd(long a, long b) 
    {
        if (a == 0)
            return b;    
        return gcd(b%a, a);
    }
    static void pn(Object o) { System.out.println(o); } 
    static void p(Object o) { System.out.print(o); }
    static void flush() { System.out.flush(); }

    static void debugInt(int[] arr)
    {
        for(int i=0;i<arr.length;++i)
            System.out.print(arr[i]+" ");
        System.out.println();
    }
    static void debugIntInt(int[][] arr)
    {
        for(int i=0;i<arr.length;++i)
        {
            for(int j=0;j<arr[0].length;++j)
                System.out.print(arr[i][j]+" ");
            System.out.println();
        }
        System.out.println();
    }
    static void debugLong(long[] arr)
    {
        for(int i=0;i<arr.length;++i)
            System.out.print(arr[i]+" ");
        System.out.println();
    }
    static void debugLongLong(long[][] arr)
    {
        for(int i=0;i<arr.length;++i)
        {
            for(int j=0;j<arr[0].length;++j)
                System.out.print(arr[i][j]+" ");
            System.out.println();
        }
        System.out.println();
    }
    static long[] takeLong(int n, FastScanner fs)
    {
        long[] arr=new long[n];
        for(int i=0;i<n;++i)
            arr[i]=fs.nextLong();
        return arr;
    } 
    static long[][] takeLongLong(int m, int n, FastScanner fs)
    {
        long[][] arr=new long[m][n];
        for(int i=0;i<m;++i)
            for(int j=0;j<n;++j)
                arr[i][j]=fs.nextLong();
        return arr;
    } 
    static int[] takeInt(int n, FastScanner fs)
    {
        int[] arr=new int[n];
        for(int i=0;i<n;++i)
            arr[i]=fs.nextInt();
        return arr;
    } 
    static int[][] takeIntInt(int m, int n, FastScanner fs)
    {
        int[][] arr=new int[m][n];
        for(int i=0;i<m;++i)
            for(int j=0;j<n;++j)
                arr[i][j]=fs.nextInt();
        return arr;
    } 
    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }
    static boolean[] sieve()
    {
        int size=(int)(1e5+5);
        boolean[] isPrime=new boolean[size];
        Arrays.fill(isPrime, true);
        for(int i=2;i<size;++i)
            for(int j=2*i;isPrime[i]==true && j<size;j+=i)
                isPrime[j]=false;

        return isPrime;
    }
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                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());
        }
    }


}
class Pair
{
    
}