description: 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. 
solution: 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;
  	}
  }