human
Can you provide a Python code to print the answer as follows: given the following:
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 —...
Solve the task in PYTHON3.
assistant
#Here is Python code to print the answer as follows:
.

t = int(input())
for _ in range(t):
    n = int(input())
    B = list(map(int,input().split()))
    nsum = n * (n+1) / 2
    if sum(B) % nsum == 0:
        S = sum(B) // nsum
        ans = list()
        ll = 0
        for i in range(n):
            if i == 0:
                kk = B[n-1]
            else:
                kk = B[i-1]
            k = ((S-B[i]+kk) / n)
            if k < 1 or k != int(k):
                ll = 1
                break
            ans.append(k)
        if ll == 1:
            print('NO')
        else:
            print('YES')
            for i in ans:
                print(int(i),end=' ')
    else:
        print('NO')






# import numpy as np
# def eliminate(r1, r2, col, target=0):
#     fac = (r2[col]-target) / r1[col]
#     for i in range(len(r2)):
#         r2[i] -= fac * r1[i]

# def gauss(a):
#     for i in range(len(a)):
#         if a[i][i] == 0:
#             for j in range(i+1, len(a)):
#                 if a[i][j] != 0:
#                     a[i], a[j] = a[j], a[i]
#                     break
#             else:
#                 raise ValueError("Matrix is not invertible")
#         for j in range(i+1, len(a)):
#             eliminate(a[i], a[j], i)
#     for i in range(len(a)-1, -1, -1):
#         for j in range(i-1, -1, -1):
#             eliminate(a[i], a[j], i)
#     for i in range(len(a)):
#         eliminate(a[i], a[i], i, target=1)
#     return a

# def inverse(a):
#     tmp = [[] for _ in a]
#     for i,row in enumerate(a):
#         assert len(row) == len(a)
#         tmp[i].extend(row + [0]*i + [1] + [0]*(len(a)-i-1))
#     gauss(tmp)
#     ret = []
#     for i in range(len(tmp)):
#         ret.append(tmp[i][len(tmp[i])//2:])
#     return ret

# t = int(input())

# for _ in range(t):
#     n = int(input())
#     b = list(map(int,input().split()))
#     B = np.array([[b[i]] for i in range(n)])
#     a = [1]
#     for i in range(n, 1, -1):
#         a.append(i)
#     A = list()
#     A.append(a)
#     for i in range(1, n):
#         temp = A[i-1][0:n-1]
#   ...