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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.lang.reflect.Array;
import java.util.*;
import java.util.stream.Stream;

public class Program {

    static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

    public static void main(String[] args) throws NumberFormatException, IOException {

        int cases = Integer.parseInt(reader.readLine());
        int mod = 998244353;

        while(cases-- > 0) {

            String[] firstLine = reader.readLine().split(" ");
            int n = Integer.parseInt(firstLine[0]);
            //int k = Integer.parseInt(firstLine[1]);
            int[] arr = convertToIntPrimitiveArray(reader.readLine().split(" "));

            int sum = (Arrays.stream(arr).sum());

            int deno = (n*(n+1))/2;

            if(sum%deno != 0) {
                printNo();
                continue;
            }

            sum /= deno;
            int[] ans = new int[n];
            boolean pos = true;

            for(int i=1;i<=n;i++) {
                int a = arr[(i-1)%n];
                int b = arr[i%n];
                int diff = b-a;
                if((sum-diff)%n != 0) {
                    pos = false;
                    break;
                }
                ans[i%n] = (sum-diff)/n;

                if(ans[i%n] <= 0) {
                    pos = false;
                    break;
                }
            }

            if(!pos) {
                printNo();
                continue;
            }

            printYes();

            for(int i=0;i<n;i++) {
                out.append(ans[i] + " ");
            }

            out.append("\n");

        }

        out.flush();

    }

    public static int[] convertToIntPrimitiveArray(String[] str) {
        return Stream.of(str).mapToInt(Integer::parseInt).toArray();
    }

    public static Integer[] convertToIntArray(String[] str) {
        Integer[] arr = new Integer[str.length];
        for(int i=0;i<str.length;i++) {
            arr[i] = Integer.parseInt(str[i]);
        }
        return arr;
    }

    public static Long[] convertToLongArray(String[] str) {
        Long[] arr = new Long[str.length];
        for(int i=0;i<str.length;i++) {
            arr[i] = Long.parseLong(str[i]);
        }
        return arr;
    }

    public static long[] convertToLongPrimitiveArray(String[] str) {
        return Stream.of(str).mapToLong(Long::parseLong).toArray();
    }

    public static void printYes() throws IOException {
        out.append("YES" + "\n");
    }

    public static void printNo() throws IOException {
        out.append("NO" + "\n");
    }

    public static void printNumber(long num) throws IOException {
        out.append(num + "\n");
    }

    public static long hcf(long a, long b) {
        if(b==0) return a;
        return hcf(b, a%b);
    }

    public static int findSet(int[] parent, int[] rank, int v) {
        if(v==parent[v]) {
            return v;
        }
        parent[v] = findSet(parent, rank, parent[v]);
        return parent[v];
    }

    public static void unionSet(int[] parent, int[] rank, int a, int b) {

        a = findSet(parent, rank, a);
        b = findSet(parent, rank, b);

        if(a == b) {
            return;
        }

        if(rank[a] < rank[b]) {
            int temp = a;
            a = b;
            b = temp;
        }

        parent[b] = a;
        if(rank[a] == rank[b]) {
            rank[a]++;
        }

    }

    public static void makeSet(int[] parent, int[] rank, int v) {
        parent[v] = v;
        rank[v] = 0;
    }

    public static long modularDivision(long a, long b, int mod) {
        if(a==0) return 1;
        a %= mod;
        long res = 1L;
        while(b > 0) {
            if((b&1)==1) {
                res = (res * a)%mod;
            }
            a = (a*a)%mod;
            b >>= 1;
        }
        return res;
    }

    public static void customSort(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        Arrays.sort(arr);
        return;
    }

    public static long[] factorial(int n, int mod) {
        long[] fact = new long[n+1];
        fact[0] = 1;
        for(int i=1;i<fact.length;i++) {
            fact[i] = (i*fact[i-1] + mod)%mod;
        }
        return fact;
    }

}