E. Singers' Tourtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputn 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.InputThe first line contains one integer t (1 \le t \le 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 \le n \le 4 \cdot 10^4) — the number of cities. The second line contains n integers b_1, b_2, \dots, b_n (1 \le b_i \le 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.OutputFor 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, \dots, a_n of n integers, where a_i (1 \le a_i \le 10^{9}) is the initial duration of repertoire of the i-th singer. If there are multiple answers, print any of them.ExampleInput
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 
NoteLet's consider the 1-st test case of the example:  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;  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;  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. 
4
3
12 16 14
1
1
3
1 2 3
6
81 75 75 93 93 87

YES 3 1 3  YES 1  NO YES 5 5 4 1 4 5  
['constructive algorithms', 'math', '*1700']