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. 
/*
                       _oo0oo_
                      o8888888o
                      88" . "88
                      (| -_- |)
                      0\  =  /0
                    ___/`---'\___
                  .' \\|     |// '.
                 / \\|||  :  |||// \
                / _||||| -:- |||||- \
               |   | \\\  -  /// |   |
               | \_|  ''\---/''  |_/ |
               \  .-\__  '-'  ___/-. /
             ___'. .'  /--.--\  `. .'___
          ."" '<  `.___\_<|>_/___.' >' "".
         | | :  `- \`.;`\ _ /`;.`/ - ` : | |
         \  \ `_.   \_ __\ /__ _/   .-` /  /
     =====`-.____`.___ \_____/___.-`___.-'=====
                       `=---='
 
*/

import java.util.*;
import java.math.*;
import java.io.*;
import java.lang.Math.*;

public class KickStart2020 {
	 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());
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);

	}
	static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}

	public static class Pair implements Comparable<Pair> {
		public int index;
		public String value;

		public Pair(int index,String value) {
			this.index = index;
			this.value = value;
		}

		@Override
		public int compareTo(Pair other) {
			// multiplied to -1 as the author need descending sort order
			if(other.index < this.index) return -1;
			if(other.index > this.index) return 1;
			return 0;
		}
		@Override
		public String toString() {
			return this.index + " " + this.value;
		}
	}
	static boolean isPrime(long d) {
		if (d == 3)
			return false;
		for (int i = 2; i <= (long) Math.sqrt(d); i++) {
			if (d % i == 0)
				return false;
		}
		return true;
	}
	static void decimalTob(int n, int k, Stack<Integer> ss) {
          int x = n % k;
          int y = n / k;
          ss.push(x);
          if(y > 0) {
        	   decimalTob(y, k, ss);
          }
	}
	static long powermod(long x, long y, long mod) {
		long ans = 1;
		x = x % mod;
		if (x == 0)
			return 0;
		int i = 1;
		while (y > 0) {
			if ((y & 1) != 0)
				ans = (ans * x) % mod;
			y = y >> 1;
			x = (x * x) % mod;
		}
		return ans;
	}
	static long power(long x, long y)
	{
	    long res = 1;
	    while (y > 0)
	    {
	        if ((y & 1) != 0)
	            res = res * x;	  
	        y = y >> 1; 
	        x = x * x;  
	    }
	    return res;
	}
	public static void main(String[] args) throws Exception {
		FastReader sc = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int t = sc.nextInt();
		outerloop:
			while(t-- > 0) {
             int n = sc.nextInt();
             int brr[] = new int[n];
             long sum = 0;
             for(int i = 0; i < n; i++) {
            	 sum += brr[i] = sc.nextInt();
             }
             int total = n * (n + 1) / 2;
             if(sum % total == 0 && sum / total >= n) {
            	 long z = sum / total;
            	 long arr[] = new long[n];
            	 for(int i = 0; i < n; i++) {
            		 long k = brr[i] - brr[(i + 1) % n] + z;
            		 if(k > 0 && k % n == 0) arr[(i + 1) % n] = k / n;
            		 else {
            			 out.println("NO");
            			 continue outerloop;
            		 }
            	 }
            	 out.println("YES");
            	 for(int i = 0; i < n; i++) out.print(arr[i] + " ");
            	 out.println();
             }
             else out.println("NO");
			}
		out.close();
	}
}