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 io, os
  import sys 
  from sys import stdin
  
  from bisect import bisect_left, bisect_right
  from collections import defaultdict, deque, namedtuple
  from heapq import heappush, heappop
  from math import gcd, ceil, floor, factorial, sqrt
  from itertools import combinations, permutations
  
  input = sys.stdin.buffer.readline
  # input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
  # input = sys.stdin.readline
  
  def work():
      ans = 0 
  
      return 
  
  # sys.setrecursionlimit(200010)
  # https://codeforces.com/contest/1618/problem/E
  def main():
      test = int(input())
  
      for idt in range(test):
          n = int(input())
          # n, m = map(int, input().split())
          b = list(map(int, input().split()))
          flag = True 
          coe = (n + 1) * n // 2 
          if sum(b) % coe != 0:
              flag = False 
          
          if not flag:
              print("NO")
              continue 
  
          tot = sum(b) // coe
          a = [0] * (n + 1)
          b = [0] + b 
          for i in range(2, n + 1):
              diff = b[i - 1] - b[i]
              if (diff + tot) % n != 0:
                  flag = False 
                  break 
              a[i] = (diff + tot) // n 
              if a[i] < 1 or a[i] > 10 ** 9:
                  flag = False 
                  break 
  
          a[1] = tot - sum(a)
          if a[1] < 1 or a[1] > 10 ** 9:
              flag = False 
          if flag:
              print("YES")
              for i in range(1, n + 1):
                  print(a[i], end=" ")
              print()
          else:
              print("NO")
      
      return 
  
  
  if __name__ == '__main__':
      main()