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 Solution {
    static int M = 998244353; //1_000_000_007;
    static Random rng = new Random();

    private static int[] testCase(int n, int[] b) {
        int[] ans = new int[n];
        long sum = 0, s, na;

        for (int bi : b) {
            sum += bi;
        }

        if (sum % ((n * (n + 1)) >> 1) == 0) {
            s = sum / ((n * (n + 1)) >> 1);

            for (int i = 0; i < n; i++) {
                na = (i == 0 ? b[n - 1] : b[i - 1]) - (b[i] - s);

                if (na % n != 0) {
                    return null;
                }

                ans[i] = (int) (na / n);
                
                if (ans[i] <= 0) {
                    return null;
                }
            }

            return ans;
        } else {
            return null;
        }
    }

    public static void main(String[] args) {
        FastScanner in = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int t = in.nextInt();  // Scanner has functions to read ints, longs, strings, chars, etc.
        //in.nextLine();
        for (int tt = 1; tt <= t; ++tt) {
            int n = in.nextInt();
            int[] b = in.readArray(n);

            int[] ans = testCase(n, b);

            if (ans == null) {
                out.println("NO");
            } else {
                out.println("YES");

                for (int an : ans) {
                    out.print(an + " ");
                }

                out.println();
            }
        }

        out.close();
    }

    private static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        boolean hasNext() {
            return st.hasMoreTokens();
        }

        char[] readCharArray(int n) {
            char[] arr = new char[n];
            try {
                br.read(arr);
                br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return arr;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }

    private static void sort(int[] arr) {
        int temp, idx;

        for (int i = arr.length - 1; i > 0; i--) {
            idx = rng.nextInt(i + 1);

            temp = arr[i];
            arr[i] = arr[idx];
            arr[idx] = temp;
        }

        Arrays.sort(arr);
    }

    private static void sort(long[] arr) {
        long temp;
        int idx;

        for (int i = arr.length - 1; i > 0; i--) {
            idx = rng.nextInt(i + 1);

            temp = arr[i];
            arr[i] = arr[idx];
            arr[idx] = temp;
        }

        Arrays.sort(arr);
    }

    private static <T> void sort(T[] arr) {
        T temp;
        int idx;

        for (int i = arr.length - 1; i > 0; i--) {
            idx = rng.nextInt(i + 1);

            temp = arr[i];
            arr[i] = arr[idx];
            arr[idx] = temp;
        }

        Arrays.sort(arr);
    }

    private static <T> void sort(T[] arr, Comparator<? super T> cmp) {
        T temp;
        int idx;

        for (int i = arr.length - 1; i > 0; i--) {
            idx = rng.nextInt(i + 1);

            temp = arr[i];
            arr[i] = arr[idx];
            arr[idx] = temp;
        }

        Arrays.sort(arr, cmp);
    }

    private static <T extends Comparable<? super T>> void sort(List<T> list) {
        T temp;
        int idx;

        for (int i = list.size() - 1; i > 0; i--) {
            idx = rng.nextInt(i + 1);

            temp = list.get(i);
            list.set(i, list.get(idx));
            list.set(idx, temp);
        }

        Collections.sort(list);
    }

    private static <T> void sort(List<T> list, Comparator<? super T> cmp) {
        T temp;
        int idx;

        for (int i = list.size() - 1; i > 0; i--) {
            idx = rng.nextInt(i + 1);

            temp = list.get(i);
            list.set(i, list.get(idx));
            list.set(idx, temp);
        }

        Collections.sort(list, cmp);
    }

    class DSU {
        int[] parent, rank;

        public DSU(int n) {
            parent = new int[n];
            rank = new int[n];

            for (int i = 0; i < n; i++) {
                parent[i] = i;
            }
        }

        public int find(int i) {
            if (parent[i] == i) {
                return i;
            } else {
                int res = find(parent[i]);
                parent[i] = res;

                return res;
            }
        }

        public boolean isSameSet(int i, int j) {
            return find(i) == find(j);
        }

        public void union(int i, int j) {
            int iParent = find(i), jParent = find(j);

            if (iParent != jParent) {
                if (rank[iParent] > rank[jParent]) {
                    parent[jParent] = iParent;
                } else {
                    parent[iParent] = jParent;

                    if (rank[iParent] == rank[jParent]) {
                        rank[jParent]++;
                    }
                }
            }
        }
    }
}