human
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 —...":


 ... Can you provide a Python program to print the answer as follows:?
assistant
#Here is Python program to print the answer as follows:
.
 
def main():
    
    t = int(input())
    allans = []
    for _ in range(t):
        n = int(input())
        b = readIntArr()
        base = ((1 + n) * n) // 2 # 1 + 2 + ... + n
        total = sum(b)
        if total % base != 0:
            allans.append(['NO'])
            continue
        total2 = total // base # a1 + a2 + a3 + ...
        a = [-1] * n
        ok = True
        for i in range(n):
            naVal = b[i - 1] - (b[i] - total2) # n * a
            aVal = naVal // n
            a[i] = aVal
            if not (naVal % n == 0 and 1 <= aVal <= 1000000000):
                allans.append(['NO'])
                ok = False
                break
        if ok:
            allans.append(['YES'])
            allans.append(a)
    multiLineArrayOfArraysPrint(allans)
    
    return

import sys
input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
# input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.

def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return [float(x) for x in input().split()]
 
def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
    dv=defaultValFactory;da=dimensionArr
    if len(da)==1:return [dv() for _ in range(da[0])]
    else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
 
def queryInteractive(i,j):
    print('? {} {}'.format(i,j))
    sys.stdout.flush()
    return int(input())
 
def answerInteractive(i,j,k):
    print('! {} {} {}'.format(i,j,k))
    sys.stdout.flush()
 
inf=float('inf')
# MOD=10**9+7
# MOD=998244353

from math import gcd,floor,ceil
import math
# from math import floor,ceil # for Python2
 
for _abc in range(1):
    main()