human
Write me a Python program to print the answer as follows: given the following:
PYTHON3 solution for "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 —...":
assistant
#Here is Python program to print the answer as follows:
.
 def find(n, L):
    if n == 1:
        return True, [str(L[0]), ]
    total = 0
    for elem in L:
        total += elem
    sum = total * 2 /n /(n+1)
    if sum != int(sum):
        return False, 0
    A = []
    first = (sum - L[0] + L[-1])/n
    if first != int(first) or first <= 0:
        return False, 0
    A.append(str(int(first)))
    for i in range(1, n):
        cur = (sum - L[i] + L[i-1])/n
        if cur != int(cur) or cur <= 0:
            return False, 0
        A.append(str(int(cur)))
    return True, A

cases = int(input())
for i in range(cases):
    n = int(input())
    l = input().split( )
    L = []
    for elem in l:
        L.append(int(elem))
    now = find(n, L)
    if now[0]:
        print('YES')
        print(' '.join(now[1]))
    else:
        print('NO')