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 q5 {
    public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//    public static long mod = 1000000007;

    public static void solve() throws Exception {
        String[] parts = br.readLine().split(" ");
        long n = Integer.parseInt(parts[0]);

        long[] arr = new long[(int)n];

        long sum = 0;
        parts = br.readLine().split(" ");
        for (int i = 0; i < n; i++) {
            arr[i] = Integer.parseInt(parts[i]);
            sum += arr[i];
        }

        if(n == 1){
            System.out.println("YES");
            System.out.println(arr[0]);
            return;
        }
        if(n == 2){
            long a = -arr[0] + 2 * arr[1];
            long b = 2 * arr[0] - arr[1];

            if(a <= 0 || b <= 0 || a % 3 != 0 || b % 3 != 0) System.out.println("NO");
            else{
                System.out.println("YES");
                System.out.println((a / 3) + " " + (b / 3));
            }
            return;
        }

        long det = (n * n * (n + 1)) / 2;

        long v1 = (n * (n + 1)) / 2 + 1;
        long v2 = 2 - v1;

        int idx1 = 0,idx2 = (int)n - 1;
        StringBuilder ans = new StringBuilder();
        for(int i = 0;i < n;i++){
            long val = sum - arr[idx1] - arr[idx2];
            val += arr[idx1]  * v2;
            val += arr[idx2] * v1;

            idx1  = (idx1 + 1) % (int)n;
            idx2  = (idx2 + 1) % (int)n;

            if(val <= 0 || val % det != 0){
                System.out.println("NO");
                return;
            }

            ans.append(val / det).append(" ");
        }
        System.out.println("YES");
        System.out.println(ans);
    }

    public static void main(String[] args) throws Exception {
        int tests = Integer.parseInt(br.readLine());
        for (int test = 1; test <= tests; test++) {
            solve();
        }
    }

//    public static void sort(int[] arr){
//        ArrayList<Integer> temp = new ArrayList<>();
//        for(int val : arr) temp.add(val);
//
//        Collections.sort(temp);
//
//        for(int i = 0;i < arr.length;i++) arr[i] = temp.get(i);
//    }
//    public static void sort(long[] arr){
//        ArrayList<Long> temp = new ArrayList<>();
//        for(long val : arr) temp.add(val);
//
//        Collections.sort(temp);
//
//        for(int i = 0;i < arr.length;i++) arr[i] = temp.get(i);
//    }
//
//    public static long power(long a,long b,long mod){
//        if(b == 0) return 1;
//
//        long p = power(a,b / 2,mod);
//        p = (p * p) % mod;
//
//        if(b % 2 == 1) return (p * a) % mod;
//        return p;
//    }
//
//    public static int GCD(int a,int b){
//        return b == 0 ? a : GCD(b,a % b);
//    }
//    public static long GCD(long a,long b){
//        return b == 0 ? a : GCD(b,a % b);
//    }
//
//    public static int LCM(int a,int b){
//        return a * b / GCD(a,b);
//    }
//    public static long LCM(long a,long b){
//        return a * b / GCD(a,b);
//    }
}
