description: 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. 
solution: import java.io.*;
  import java.util.*;
  import java.text.*;
  import java.math.*;
  import java.util.regex.*;
   
  public class Codechef{
  	static Scanner in=new Scanner();
  	static long mod = 1000000007;
  	static ArrayList<ArrayList<Integer>> adj;
  	public static void main(String[] args) throws Exception{
  		int z=in.readInt();
  		while(z-->0) {
  			solve();
  		}
  	}
  	static void solve() {
  		int n=in.readInt();
  		long a[]=nla(n);
  		long sum=0;
  		for(long i:a) {
  			sum+=i;
  		}
  		long nn=n*(n+1)/2;
  		boolean flag=true;
  		if(sum%nn!=0) {
  			flag=false;
  		}
  		sum/=nn;
  		long ans[]=new long[n];
  		for(int i=1;i<n;i++) {
  			long num=sum+a[i-1]-a[i];
  			if(num%n!=0) {
  				flag=false;
  				break;
  			}
  			ans[i]=num/n;
  		}
  		ans[0]=sum+a[n-1]-a[0];
  		if(ans[0]%n!=0) {
  			flag=false;
  		}
  		ans[0]/=n;
  		for(long i:ans) {
  			if(i<=0) {
  				flag=false;
  				break;
  			}
  		}
  		if(!flag) {
  			System.out.println("NO");
  			return;
  		}
  		System.out.println("YES");
  		for(long i: ans) {
  			System.out.print(i+" ");
  		}
  		System.out.println();
  	}
  	static int[] nia(int n){
  		int[] arr= new int[n];
  		int i=0;
  		while(i<n){
  			arr[i++]=in.readInt();
  		}
  		return arr;
  	}
  	static long[] nla(int n){
  		long[] arr= new long[n];
  		int i=0;
  		while(i<n){
  			arr[i++]=in.readLong();
  		}
  		return arr;
  	}
  	static int[] nia1(int n){
  		int[] arr= new int[n+1];
  		int i=1;
  		while(i<=n){
  			arr[i++]=in.readInt();
  		}
  		return arr;
  	}
  	static long gcd(long a, long b) {
  		if (b==0) return a;
  		return gcd(b, a%b);
  	}
  	static class Scanner{
  		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
  		StringTokenizer st=new StringTokenizer("");
  		String readString() {
  			while (!st.hasMoreTokens())
  				try {
  					st=new StringTokenizer(br.readLine());
  				} catch (IOException e) {
  					e.printStackTrace();
  				}
  			return st.nextToken();
  		}
  		double readDouble() {
  			return Double.parseDouble(readString());
  		}
  		int readInt() {
  			return Integer.parseInt(readString());
  		}
  		long readLong() {
  			return Long.parseLong(readString());
  		}
  	}	
  }