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.*;
import java.math.*;
import java.util.*;
public class P03 {   
	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());}
		float nextFloat(){return Float.parseFloat(next());}
		String nextLine(){
			String str = "";
			try {
				str = br.readLine();
			}catch(IOException e) {
				e.printStackTrace();
			}
			return str ;
		}
	}
	private static long gcd(long l, long m){
		if(m==0) {
			return l;
		}
		return gcd(m,l%m);
	}
	static void swap(long[] arr, int i, int j){
	    long temp = arr[i];
	    arr[i] = arr[j];
	    arr[j] = temp;
	}
	static int partition(long[] arr, int low, int high){	   
	    long pivot = arr[high];   
	    int i = (low - 1);
	    for(int j = low; j <= high - 1; j++){    
	        if (arr[j] < pivot){          
	            i++;
	            swap(arr, i, j);
	        }
	    }
	    swap(arr, i + 1, high);
	    return (i + 1);
	}
	static void quickSort(long[] arr, int low, int high){
	    if (low < high){  
	        int pi = partition(arr, low, high);
	        quickSort(arr, low, pi - 1);
	        quickSort(arr, pi + 1, high);
	    }
	}
	static long M = 1000000007;
	static long powe(long a,long b) {
		long res =1;
		while(b>0){
			if((b&1)!=0) {
				res=(res*a)&M;
			}
			a=(a*a)%M;
			b>>=1;
		}
		return res;
	}
	static long power(long x, long y, long p)  {
	    long res = 1; 	 
	    x = x % p; 	 
	    if (x == 0)
	      return 0; 	 
	    while (y > 0){	 	      
	      if ((y & 1) != 0)
	      res = (res * x) % p;	 	    
	      y = y >> 1; 
	      x = (x * x) % p;
	    }
	    return res;
	  }
	static boolean [] seive(int n) {
		boolean a[] = new boolean[n+1];
		Arrays.fill(a, true);
		a[0]=false;
		a[1]=false;
		for(int i =2;i<=Math.sqrt(n);i++) {
			for(int j =2*i;j<=n;j+=i) {
				a[j]=false;
			}
		}
		return a;
	}
	private static void pa(char[] cs){for(int i =0;i<cs.length;i++){System.out.print(cs[i]+" ");}System.out.println();}
	private static void pa(long[] b){for(int i =0;i<b.length;i++) {System.out.print(b[i]+" ");}System.out.println();}
	private static void pm(Character[][] a){for(int i =0;i<a.length;i++){for(int j=0;j<a[i].length;j++){System.out.print(a[i][j]);}System.out.println();}}
	private static void pa(int[] a){for(int i =0;i<a.length;i++){System.out.print(a[i]+" ");}System.out.println();}
	private static boolean isprime(int n){if (n <= 1) return false;else if (n == 2) return true;else if (n % 2 == 0) return false;for (int i = 3; i <= Math.sqrt(n); i += 2){if (n % i == 0) return false;}return true;}
	static int lb(long[] b, long a){
		  int l=-1,r=b.length;
		  while(l+1<r) {
		    int m=(l+r)>>>1;
		    if(b[m]>=a) r=m;
		    else l=m;
		  }
		  return r;
	}
	 static int ub(long a[], long x){
		    int l=-1,r=a.length;
		    while(l+1<r) {
		       int m=(l+r)>>>1;
		       if(a[m]<=x) l=m;
		       else r=m;
		    }
		    return l+1;
	}
	static //MAIN FUNCTION ------->
	ArrayList<String> alpos = new ArrayList<>();
	public static void main(String[] args) throws IOException {
		long start2 = System.currentTimeMillis();
		FastReader fs = new FastReader();
		Scanner sc = new Scanner (System.in);
		int t = fs.nextInt();
		//int t =1;
		while(t-->0) {
			int n = fs.nextInt();
			int b [] = new int [n];
			long sumn = (n*(n+1))/2;
			long sumb =0;
			for(int  i=0;i<n;i++) {
				b[i]=fs.nextInt();
				sumb+=b[i];
			}
			long suma = sumb/sumn;
			long a [] = new long [n];
			long nsuma=0;
			for(int i =1;i<n;i++) {
				a[i]=(suma-b[i]+b[i-1])/n;
				nsuma+=a[i];
			}
			a[0]=suma-nsuma;
			boolean flag = true;
			for(int i =0;i<n;i++) {
				if(a[i]<=0) {
					flag = false;
					break;
				}
			}
		//	pa(a);
			if(!flag) {
				System.out.println("NO");
			}
			else {
				System.out.println("YES");
				pa(a);
			//	System.out.println();
			}
		}  
		long end2 = System.currentTimeMillis();
	//	System.out.println("time :"+(end2-start2));
		sc.close();
	}
}



