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.BufferedReader;
  import java.io.IOException;
  import java.io.InputStreamReader;
  import java.util.Arrays;
  import java.util.Comparator;
  import java.util.HashSet;
  import java.util.List;
  import java.util.Set;
  import java.util.StringTokenizer;
   
  public class Main {
  	static FastReader fr;
  	static int arrForIndexSort[];
  	static Integer map1[];
  	static Integer map2[];
  	
  	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;
          }
      }
  	static class Pair{
  		int first;
  		int second;
  		Pair(int first, int second){
  			this.first = first;
  			this.second = second;
  		}
  		@Override
  		public boolean equals(Object b) {
  			Pair a = (Pair)b;
  			if(this.first == a.first && this.second==a.second) {
  				return true;
  			}
  			return false;
  		}
  	}
  	class PairSorter implements Comparator<Main.Pair>{
  		public int compare(Pair a, Pair b) {
  			if(a.first!=b.first) {
  				return a.first-b.first;
  			}
  			return a.second-b.second; 
  		}
  	}
  	static class DoublePair{
  		double first;
  		double second;
  		DoublePair(double first, double second){
  			this.first = first;
  			this.second = second;
  		}
  		@Override
  		public boolean equals(Object b) {
  			Pair a = (Pair)b;
  			if(this.first == a.first && this.second==a.second) {
  				return true;
  			}
  			return false;
  		}
  	}
  	class DoublePairSorter implements Comparator<Main.DoublePair>{
  		public int compare(DoublePair a, DoublePair b) {
  			 if(a.second>b.second) {
  				 return 1;
  			 }
  			 else if(a.second<b.second) {
  				 return -1;
  			 }
  			 return 0;
  		}
  	}
  	class IndexSorter implements Comparator<Integer>{
  		public int compare(Integer a, Integer b) {
  			//desc
  			if(arrForIndexSort[b]==arrForIndexSort[a]) {
  				return b-a;
  			}
  			return arrForIndexSort[b]-arrForIndexSort[a];
  		}
  	}
  	class ListSorter implements Comparator<List>{
  		public int compare(List a, List b) {
  			return b.size()-a.size(); 
  		}
  	}
  	static class DisjointSet{
  		int[] dsu;
  		public DisjointSet(int n) {
  			makeSet(n);
  		}
  		public void makeSet(int n) {
  			dsu = new int[n+1];
  			//*** 1 Based indexing ***
  			for(int i=1;i<=n;i++) {
  				dsu[i] = -1;
  			}
  		}
  		public int find(int i) {
  			while(dsu[i] > 0) {
  				i = dsu[i];
  			}
  			return i;
  		}
  		public void union(int i, int j) {
  			int iRep = find(i);
  			int jRep = find(j);
  			if(iRep == jRep) {
  				return;
  			}
  			if(dsu[iRep]>dsu[jRep]) {
  				dsu[jRep] += dsu[iRep];
  				dsu[iRep] = jRep;
  			}
  			else {
  				dsu[iRep] += dsu[jRep];
  				dsu[jRep] = iRep;
  			}
  		}
  	}
  	public static void main(String[] args) {
  		fr = new FastReader();
  		int T = 1;
  		T = fr.nextInt();
  		int t1 = T;
  		while (T-- > 0) {
  			solve();
  		}
  	}
  	public static void solve() {
  		int n = fr.nextInt();
  		int b[] = new int[n];
  		int a[] = new int[n];
  		long sum = 0;
  		for(int i=0;i<n;i++) {
  			b[i] = fr.nextInt();
  			sum += b[i];
  		}
  		int count = n*(n+1);
  		count/=2;
  		if(sum%count != 0) {
  			System.out.println("NO");
  		}
  		else {
  			sum/=count;
  			int i =0;
  			for(i=0;i<n;i++) {
  				long diff = b[i] - b[(n+i-1)%n];
  				int ai = (int) ((sum-diff)/n);
  				if(ai<=0 || (sum-diff)%n !=0) {
  					break;
  				}
  				a[i] = ai;
  			}
  			if(i==n) {
  				System.out.println("YES");
  				System.out.println(Arrays.toString(a).replaceAll("\\,|\\[|\\]", ""));
  			}
  			else {
  				System.out.println("NO");
  			}		
  		}
  	}
  
  }