B' 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 in [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 cdot a_i minutes, ..., in the ((i + k) bmod n + 1) -th town the duration of the concert will be (k + 2) cdot a_i , ..., in the town ((i + n - 2) bmod n + 1) -- n cdot 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. 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 cdot 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 cdot 10^5 . 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 sin'...