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: sr=lambda: input()
  ir=lambda: int(sr())
  lr=lambda: list(map(int, sr().split()))
  
  inf = 10**18
  # mod = 10**9+7
  mod = 998244353
  
  if __name__=='__main__':
      test = ir()
      for t in range(test):
          n=ir()
          b=lr()
          if n == 1:
              print("Yes")
              print(b[0])
              continue
          b_sub = []
          b_sub.append(b[0]-b[-1])
          for i in range(n-1):
              b_sub.append(b[i+1]-b[i])
  
          B_sub = []
          B_sub.append(b_sub[0]-b_sub[-1])
          for i in range(n-1):
              B_sub.append(b_sub[i+1]-b_sub[i])
  
          flg=True
          a_sub = []
          for num in B_sub:
              if num%n != 0:
                  flg = False
                  break
              a_sub.append(num//n)
          if not flg:
              print("No")
              continue
  
          a_sum = [a_sub[0]]
          a_sub.reverse()
          for i in range(n-1):
              a_sum.append(a_sum[-1]+a_sub[i])
          a_sum.reverse()
          x = 0
          for i in range(n):
              x += (n-i)*a_sum[i]
          tmp = n*(n+1)//2
          if (b[-1]-x) % tmp == 0:
              a1 = (b[-1]-x)//tmp
              ans=[]
              for num in a_sum:
                  ans.append(a1+num)
              flg = True
              for num in ans:
                  if num <= 0:
                      flg = False
              if flg:
                  print("Yes")
                  print(*ans, sep=" ")
              else:
                  print("No")
          else:
              print("No")
  