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.util.*;
import java.io.*;

public class Practice {
	static boolean multipleTC = true;
	FastReader in;
	PrintWriter out;

	static int mod = (int) (1e9 + 7);
	int mod2 = 998244353;
	int parent[];
	int rank[];

	public static void main(String[] args) throws Exception {
		new Practice().run();
	}

	void run() throws Exception {
		in = new FastReader();
		out = new PrintWriter(System.out);
		int T = (multipleTC) ? ni() : 1;
		pre();
		for (int t = 1; t <= T; t++)
			solve(t);
		out.flush();
		out.close();
	}

	void pre() throws Exception {
	}

	void solve(int TC) throws Exception {
		int n = ni();
		long arr[] = readArr(n);
		long sum = sum(arr);
		long sum2 = (n * (n + 1)) / 2;
		if (sum % sum2 != 0) {
			pn("NO");
		} else {
			long sum3 = sum / sum2;
			long ans[] = new long[n];
			for (int i = 0; i < n; i++) {
				int nextIdx = (i + 1) % n;
				if ((sum3 - (arr[nextIdx] - arr[i])) >= 0 || (sum3 - (arr[nextIdx] - arr[i])) % n != 0) {
					pn("NO");
					return;
				}
				ans[nextIdx] = (sum3 - (arr[nextIdx] - arr[i])) / n;
			}
			pn("YES");
			pn(printArr(ans));
		}

	}

	void union(int u, int v) {
		u = findParent(u);
		v = findParent(v);
		if (rank[u] > rank[v]) {
			parent[v] = u;
		} else if (rank[u] < rank[v]) {
			parent[u] = v;
		} else {
			parent[v] = u;
			rank[u]++;
		}
	}

	int findParent(int v) {
		if (v == parent[v])
			return v;
		return parent[v] = findParent(parent[v]);
	}

	StringBuilder printArr(int arr[]) {
		StringBuilder sb = new StringBuilder();
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			sb.append(arr[i] + " ");
		}
		return sb;
	}

	StringBuilder printArr(long arr[]) {
		StringBuilder sb = new StringBuilder();
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			sb.append(arr[i] + " ");
		}
		return sb;
	}

	class pair {
		int x, y;

		pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public String toString() {
			return " " + x + ", " + y + "]";
		}

	}

	class pairL {
		long x, y;

		pairL(long x, long y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public String toString() {
			return " " + x + ", " + y + "]";
		}

	}

	boolean isSorted(int arr[]) {
		for (int i = 0; i < arr.length - 1; i++) {
			if (arr[i] > arr[i + 1]) {
				return false;
			}
		}
		return true;
	}

	void swap(int arr[], int x, int y) {
		int t = arr[x];
		arr[x] = arr[y];
		arr[y] = t;
	}

	static int bitCount(int x) {
		return x == 0 ? 0 : (1 + bitCount(x & (x - 1)));
	}

	void sort(long arr[]) {
		ArrayList<Long> list = new ArrayList<>();
		for (int i = 0; i < arr.length; i++)
			list.add(arr[i]);
		Collections.sort(list);
		for (int i = 0; i < arr.length; i++)
			arr[i] = list.get(i);
	}

	static void dbg(Object... o) {
		System.err.println(Arrays.deepToString(o));
	}

	ArrayList<Long> primeFactorization(long n) {
		ArrayList<Long> factorization = new ArrayList<>();
		while (n % 2 == 0) {
			factorization.add(2L);
			n /= 2;
		}
		for (long d = 3; d * d <= n; d += 2) {
			while (n % d == 0) {
				factorization.add(d);
				n /= d;
			}
		}
		if (n > 1)
			factorization.add(n);
		return factorization;
	}

	public static boolean isPrime(long n) {
		if (n < 2)
			return false;
		if (n == 2 || n == 3)
			return true;
		if (n % 2 == 0 || n % 3 == 0)
			return false;
		long sqrtN = (long) Math.sqrt(n) + 1;
		for (long i = 6L; i <= sqrtN; i += 6) {
			if (n % (i - 1) == 0 || n % (i + 1) == 0)
				return false;
		}
		return true;
	}

	public static long gcd(long a, long b) {
		if (a > b)
			a = (a + b) - (b = a);
		if (a == 0L)
			return b;
		return gcd(b % a, a);
	}

	public long binaryExpo(long base, long exp) {
		long res = 1;
		while (exp > 0) {
			if ((exp & 1) == 1)
				res = res * base;
			base = base * base;
			exp >>= 1;
		}
		return res;
	}

	public long pow(long base, long exp, long MOD) {
		base %= MOD;
		long res = 1;
		while (exp > 0) {
			if ((exp & 1) == 1)
				res = res * base % MOD;
			base = base * base % MOD;
			exp >>= 1;
		}
		return res;
	}

	public static long totient(long n) {
		long result = n;
		for (int p = 2; p * p <= n; ++p)
			if (n % p == 0) {
				while (n % p == 0)
					n /= p;
				result -= result / p;
			}
		if (n > 1)
			result -= result / n;
		return result;
	}

	int bit(long n) {
		return (n == 0) ? 0 : (1 + bit(n & (n - 1)));
	}

	public long max(long... arr) {
		long max = arr[0];
		for (long itr : arr)
			max = Math.max(max, itr);
		return max;
	}

	public int max(int... arr) {
		int max = arr[0];
		for (int itr : arr)
			max = Math.max(max, itr);
		return max;
	}

	public long min(long... arr) {
		long min = arr[0];
		for (long itr : arr)
			min = Math.min(min, itr);
		return min;
	}

	public int min(int... arr) {
		int min = arr[0];
		for (int itr : arr)
			min = Math.min(min, itr);
		return min;
	}

	public long sum(long... arr) {
		long sum = 0;
		for (long itr : arr)
			sum += itr;
		return sum;
	}

	public long sum(int... arr) {
		long sum = 0;
		for (int itr : arr)
			sum += itr;
		return sum;
	}

	void p(Object o) {
		out.print(o);
	}

	void pn(Object o) {
		out.println(o);
	}

	void pni(Object o) {
		out.println(o);
		out.flush();
	}

	String n() throws Exception {
		return in.next();
	}

	String nln() throws Exception {
		return in.nextLine();
	}

	int ni() throws Exception {
		return Integer.parseInt(in.next());
	}

	long nl() throws Exception {
		return Long.parseLong(in.next());
	}

	long[] readArr(int n) throws Exception {
		long arr[] = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nl();
		}
		return arr;
	}

	double nd() throws Exception {
		return Double.parseDouble(in.next());
	}

	class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public FastReader(String s) throws Exception {
			br = new BufferedReader(new FileReader(s));
		}

		String next() throws Exception {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new Exception(e.toString());
				}
			}
			return st.nextToken();
		}

		String nextLine() throws Exception {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				throw new Exception(e.toString());
			}
			return str;
		}
	}
}