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 — for 6 minutes, in the 3-rd — for 9 minutes; 
  2. 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; 
  3. 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. 
import io, os
import sys 
from sys import stdin

from bisect import bisect_left, bisect_right
from collections import defaultdict, deque, namedtuple
from heapq import heappush, heappop
from math import gcd, ceil, floor, factorial, sqrt
from itertools import combinations, permutations

input = sys.stdin.buffer.readline
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# input = sys.stdin.readline

def work():
    ans = 0 

    return 

# sys.setrecursionlimit(200010)
# https://codeforces.com/contest/1618/problem/E
def main():
    test = int(input())

    for idt in range(test):
        n = int(input())
        # n, m = map(int, input().split())
        b = list(map(int, input().split()))
        flag = True 
        coe = (n + 1) * n // 2 
        if sum(b) % coe != 0:
            flag = False 
        
        if not flag:
            print("NO")
            continue 

        tot = sum(b) // coe
        a = [0] * (n + 1)
        b = [0] + b 
        for i in range(2, n + 1):
            diff = b[i - 1] - b[i]
            if (diff + tot) % n != 0:
                flag = False 
                break 
            a[i] = (diff + tot) // n 
            if a[i] < 1 or a[i] > 10 ** 9:
                flag = False 
                break 

        a[1] = tot - sum(a)
        if a[1] < 1 or a[1] > 10 ** 9:
            flag = False 
        if flag:
            print("YES")
            for i in range(1, n + 1):
                print(a[i], end=" ")
            print()
        else:
            print("NO")
    
    return 


if __name__ == '__main__':
    main()