human
Give me a Python code 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 code to print the answer as follows:
.
 def summ(q):
    return int((q+1)*q/2)
t=int(input())
for i in range(t):
    n=int(input())
    b=[0]*n
    a=list(map(int,input().split()))
    s=sum(a)
    l=summ(n)
    e=0
    m=0
    if s%l==0:
        m=s//l
    else:
        e=-1
    b[0]=a[0]-a[-1]-m
    ss=-1
    if b[0]>0:
        e=-1
    else:
        b[0]=abs(b[0])
    if s<n:
        e=-1
    if b[0]<=0:
        e-=1
    else:
        if b[0]%n!=0:
            e-=1
        else:
            b[0]=b[0]//n
            ss=b[0]
    if e==0:
        for j in range(n-1):
            b[j+1]=a[j+1]-a[j]-m
            if b[j+1]>=0:
                e=-1
                break
            else:
                b[j+1]=abs(b[j+1])
            if b[j+1]<=0:
                e=-1
                break
            else:
                if b[j+1]%n!=0:
                    e=-1
                    break
                else:
                    b[j+1]=b[j+1]//n
                    if b[j+1]==0:
                        e=-1
                        break
                    else:
                        ss+=b[j+1]
    if (e==-1)or(ss!=m):
        print('NO')
    else:
        print('YES')
        for j in b:
            print(j,end=' ')
        print()