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.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])) % n != 0) {
  					pn("NO");
  					return;
  				}
  				ans[nextIdx] = (sum3 - (arr[nextIdx] - arr[i])) / n;
  			}
  			
  			for (int i = 0; i < n; i++) {
  				if (ans[i] <= 0) {
  					pn("NO");
  					return;
  				}
  			}
  			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;
  		}
  	}
  }