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.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());
		}
	}	
}