Problem: You are given a number n and an array b_1, b_2, …, b_{n+2}, obtained according to the following algorithm: 

  * some array a_1, a_2, …, a_n was guessed; 
  * array a was written to array b, i.e. b_i = a_i (1 ≤ i ≤ n); 
  * The (n+1)-th element of the array b is the sum of the numbers in the array a, i.e. b_{n+1} = a_1+a_2+…+a_n; 
  * The (n+2)-th element of the array b was written some number x (1 ≤ x ≤ 10^9), i.e. b_{n+2} = x; The 
  * array b was shuffled. 



For example, the array b=[2, 3, 7, 12 ,2] it could be obtained in the following ways: 

  * a=[2, 2, 3] and x=12; 
  * a=[3, 2, 7] and x=2. 



For the given array b, find any array a that could have been guessed initially.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second row of each test case contains n+2 integers b_1, b_2, …, b_{n+2} (1 ≤ b_i ≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output: 

  * "-1", if the array b could not be obtained from any array a; 
  * n integers a_1, a_2, …, a_n, otherwise. 



If there are several arrays of a, you can output any.

Example

Input


4
3
2 3 7 12 2
4
9 1 7 1 6 5
5
18 2 2 3 2 9 2
3
2 6 9 2 1


Output


2 3 7 
-1
2 2 2 3 9 
1 2 6 

Solution (in PYTHON3):

Solution:
import sys, math
import heapq

from collections import deque
input = sys.stdin.readline

#input
def ip(): return int(input())
def fp(): return float(input())
def sp(): return str(input().rstrip())

def mip(): return map(int, input().split())
def msp(): return map(str, input().split())

def lmip(): return list(map(int, input().split()))
def lmsp(): return list(map(str, input().split()))

#gcd, lcm
def gcd(x, y):
    while y:
        x, y = y, x % y
    return x

def lcm(x, y):
    return x * y // gcd(x, y)

#prime
def isprime(x):
    if x==1: return False
    for i in range(2, int(x**0.5)+1):
        if x%i==0:
            return False
    return True

# Union Find
# p = {i:i for i in range(1, n+1)}
def find(x):
    if x == p[x]:
        return x
    q = find(p[x])
    p[x] = q
    return q

def union(x, y):
    global n
    x = find(x)
    y = find(y)

    if x != y:
        p[y] = x

############### Main! ###############

t = ip()
while t:
    t -= 1
    n = ip()
    b = lmip()
    b.sort()
    sp = sum(b)
    sum1 = sp - b[-1]
    tr = -1
    for i in range(n+1):
        if sum1 - b[i] == b[-1]:
            tr = i
            break
    if tr<0:
        # print(sum(b[:-2]))
        if sum(b[:-2]) == b[-2]:
            for i in range(n):
                print(b[i], end=" ")
            print()
            continue
        print(-1)
        continue
    for i in range(n+1):
        if tr==i: continue
        print(b[i], end=" ")
    print()

######## Priest W_NotFoundGD ########