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.*;


public class ComdeFormces {
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		FastReader sc=new FastReader();
		BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
		int t=sc.nextInt();
		while(t--!=0) {
		long n=sc.nextLong();
		 long sum=(n*(n+1))/2;
		 long sum2=0;
		 ArrayList<Long> a=new ArrayList<>();
		 for(int i=0;i<n;i++) {
			 a.add(sc.nextLong());
			 sum2+=a.get(i);
		 }
		 if(sum2%sum==0) {
			 boolean ans=true;
			 long val=sum2/sum;
			 ArrayList<Long> arr=new ArrayList<>();
			 long tsum=0;
		 for(int i=0;i<n-1;i++) {
			 long mnval=a.get(i)-a.get(i+1)+val;
			 if(mnval%n!=0 || mnval<=0) {
				 ans=false;
				 break;
			 }
			 else {
				 arr.add(mnval/n);
				 tsum+=mnval/n;
			 }
			 
		 }
		if(val-tsum<=0)ans=false;
		 if(ans) {
			arr.add(0,val-tsum);
			log.write("YES\n");
			for(int i=0;i<arr.size();i++) {
				log.write(arr.get(i)+" ");
			}
		 }
		 else log.write("NO");
		 
		 }
		 else log.write("NO");
         
		
		 
		log.write("\n");
		log.flush();
		
		}
		
	}
static long find(int s,long a[]) {
	if(s>=a.length)return -1;
	long num=a[s];
	for(int i=s;i<a.length;i+=2) {
		num=gcd(num,a[i]);
		if(num==1 || num==0)return -1;
	}
	return  num;
}	
static long gcd(long a,long b) {
	if(b==0)return a;
	else return gcd(b,a%b);
}	
static long factmod(long n,long mod,long img) {
	if(n==0)return 1;
	long ans=1;
	long temp=1;
	while(n--!=0) {
		if(temp!=img) {
		ans=((ans%mod)*((temp)%mod))%mod;
		}
		temp++;
	}
	return ans%mod;
}	
static long eval(ArrayList<Integer> a, int k) {
	if(a.size()<1 )return 0;
	int i=a.size()-1;
	long ans=0;
	while(i>=0) {
		int temp=k;
		int prev=0;
		while(temp--!=0 && i>=0) {
			ans+=Math.abs(a.get(i)-prev);
			if(temp==0 || i==0)ans+=a.get(i);
			prev=a.get(i);
			i--;
		}
	}
	return ans;
}	
static long bs(long end ,long cnt,long prev,long n) {
	long start=1;
	long st=end;
    while(start<=end) {
    	long mid=start+(end-start)/2;
    	if(mid*cnt+prev==n)return mid;
    	else if(mid*cnt+prev>n)end=mid-1;
    	else start=mid+1;
    }
    if(start<=st && start*cnt+prev>=n)return start;
	return -1;
}	
	
	
//utils	
public static class trip{
	int a,b,c;
	public trip(int a,int b,int c) {
		this.a=a;
		this.b=b;
		this.c=c;
	}
	public int compareTo(trip q) {
		return this.c-q.c;
	}
}	
	static void mergesort(long[] a,int start,int end) {
		if(start>=end)return;
		int mid=start+(end-start)/2;
		mergesort(a,start,mid);
		mergesort(a,mid+1,end);
		merge(a,start,mid,end);
	}
	static void merge(long []a, int start,int mid,int end) {
		int ptr1=start;
		int ptr2=mid+1;
		long b[]=new long[end-start+1];
		int i=0;
		while(ptr1<=mid && ptr2<=end) {
			if(a[ptr1]<=a[ptr2]) {
				b[i]=a[ptr1];
				ptr1++;
				i++;
			}
			else {
				b[i]=a[ptr2];
				ptr2++;
				i++;
			}
		}
		while(ptr1<=mid) {
			b[i]=a[ptr1];
			ptr1++;
			i++;
		}
		while(ptr2<=end) {
			b[i]=a[ptr2];
			ptr2++;
			i++;
		}
		for(int j=start;j<=end;j++) {
			a[j]=b[j-start];
		}
	}
	public static class FastReader {

		BufferedReader b;
		StringTokenizer s;
		public FastReader() {
			b=new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {
			while(s==null ||!s.hasMoreElements()) {
				try {
					s=new StringTokenizer(b.readLine());
				}
				catch(IOException e) {
					e.printStackTrace();
				}
			}
			return s.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		String nextLine() {
			String str="";
			try {
				str=b.readLine();
			}
			catch(IOException e) {
				e.printStackTrace();
			}
			return str;
		}
		boolean hasNext() {
		    if (s != null && s.hasMoreTokens()) {
		        return true;
		    }
		    String tmp;
		    try {
		        b.mark(1000);
		        tmp = b.readLine();
		        if (tmp == null) {
		            return false;
		        }
		        b.reset();
		    } catch (IOException e) {
		        return false;
		    }
		    return true;
		}
}
public static class pair{
	int a,b;
	public pair(int a,int b) {
		this.a=a;
		this.b=b;
	}
	public int compareTo(pair b) {
		return this.a-b.a;
	}
}	
}
