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.lang.*;
import java.io.*;

public class Codechef {
	static long fans[] = new long[200001];
	static long inv[] = new long[200001];
	static long mod = 1000000007;

	static void init() {
		fans[0] = 1;
		inv[0] = 1;
		fans[1] = 1;
		inv[1] = 1;
		for (int i = 2; i < 200001; i++) {
			fans[i] = ((long) i * fans[i - 1]) % mod;
			inv[i] = power(fans[i], mod - 2);
		}
	}

	static long ncr(int n, int r) {
		return (((fans[n] * inv[n - r]) % mod) * (inv[r])) % mod;
	}

	public static void main(String[] args) throws java.lang.Exception {
		FastReader in = new FastReader(System.in);
		StringBuilder sb = new StringBuilder();
		int t = 1;
		t = in.nextInt();
		while (t > 0) {
			--t;
			int n = in.nextInt();
			long arr[] = generateArray(in, n);
			long sum = 0;
			long termsum = 0;
			for(int i = 0;i<n;i++)
			{
				sum+=arr[i];
				termsum+= (i+1);
			}
			if(sum%termsum!=0)
			{
				sb.append("NO\n");
				continue;
			}
			long sumbytermsum = sum/termsum;
			long sum2 = 0;
			long ans[] = new long[n];
			boolean poss = true;
			for(int i = 0;i<n-1;i++)
			{
			    long temp = arr[i] - arr[i+1] + sumbytermsum;
			    if(temp%n!=0 || temp/n == 0)
			    {
			    	poss = false;
			    	break;
			    }
			    else
			    {
			    	ans[i+1] = temp/n;
			    	sum2+=ans[i+1];
			    }
			}
			ans[0] = sumbytermsum - sum2;
			if(ans[0] <=0)
				poss = false;
			if(poss)
			{
				
				sb.append("YES\n");
				for(int i = 0;i<n;i++)
				{
					sb.append(ans[i]+" ");
				}
				sb.append("\n");
			}
			else 
				sb.append("NO\n");
				

		}
		System.out.print(sb);
	}

	static long power(long x, long y) {
		long res = 1; // Initialize result

		while (y > 0) {

			// If y is odd, multiply x with result
			if ((y & 1) != 0)
				res = ((res % mod) * (x % mod)) % mod;

			// y must be even now
			y = y >> 1; // y = y/2
			x = ((x % mod) * (x % mod)) % mod; // Change x to x^2
		}
		return res;
	}

	static long[] generateArray(FastReader in, int n) throws IOException {
		long arr[] = new long[n];
		for (int i = 0; i < n; i++)
			arr[i] = in.nextLong();
		return arr;
	}

	static long[][] generatematrix(FastReader in, int n, int m) throws IOException {
		long arr[][] = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				arr[i][j] = in.nextLong();
			}
		}
		return arr;
	}

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

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

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

class FastReader {

	byte[] buf = new byte[2048];
	int index, total;
	InputStream in;

	FastReader(InputStream is) {
		in = is;
	}

	int scan() throws IOException {
		if (index >= total) {
			index = 0;
			total = in.read(buf);
			if (total <= 0) {
				return -1;
			}
		}
		return buf[index++];
	}

	String next() throws IOException {
		int c;
		for (c = scan(); c <= 32; c = scan())
			;
		StringBuilder sb = new StringBuilder();
		for (; c > 32; c = scan()) {
			sb.append((char) c);
		}
		return sb.toString();
	}

	String nextLine() throws IOException {
		int c;
		for (c = scan(); c <= 32; c = scan())
			;
		StringBuilder sb = new StringBuilder();
		for (; c != 10 && c != 13; c = scan()) {
			sb.append((char) c);
		}
		return sb.toString();
	}

	char nextChar() throws IOException {
		int c;
		for (c = scan(); c <= 32; c = scan())
			;
		return (char) c;
	}

	int nextInt() throws IOException {
		int c, val = 0;
		for (c = scan(); c <= 32; c = scan())
			;
		boolean neg = c == '-';
		if (c == '-' || c == '+') {
			c = scan();
		}
		for (; c >= '0' && c <= '9'; c = scan()) {
			val = (val << 3) + (val << 1) + (c & 15);
		}
		return neg ? -val : val;
	}

	long nextLong() throws IOException {
		int c;
		long val = 0;
		for (c = scan(); c <= 32; c = scan())
			;
		boolean neg = c == '-';
		if (c == '-' || c == '+') {
			c = scan();
		}
		for (; c >= '0' && c <= '9'; c = scan()) {
			val = (val << 3) + (val << 1) + (c & 15);
		}
		return neg ? -val : val;
	}
}