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.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");
			}		
		}
	}

}