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 CPP):

Solution:
/*Rabbi Zidni Ilma*/

#include<bits/stdc++.h>
using namespace std;
#define   ll             long long
#define   scl(n)         scanf("%lld",&n)
#define   scll(n,m)      scanf("%lld %lld",&n,&m)
#define   YES            printf("YES\n")
#define   Yes            printf("Yes\n")
#define   yes            printf("yes\n")
#define   NO             printf("NO\n")
#define   No             printf("No\n")
#define   no             printf("no\n")
#define   nl             printf("\n")
#define   pb             push_back
#define   mp             make_pair
#define   frs            first
#define   scn            second
#define   pi             acos(-1)
#define   mod            1000000007
#define   CheckBit(x,k)  (x&(1ll<<k))
#define   read           freopen("input.txt","r",stdin)
#define   write          freopen("output.txt","w",stdout)

int main()
{
    ll tc,t,n,m,i,j,k;
    scl(tc);
    for(t=1;t<=tc;t++)
    {
        scl(n);
        ll b[n+2],s=0;

        for(i=0;i<(n+2);i++)
        scl(b[i]);

        sort(b,b+n+2);

        for(i=0;i<=n;i++)
        s+=b[i];

        ll x=s-b[n+1];
        bool f=0;
        for(i=0;i<=n;i++)
        {
            if(b[i]==x)
            {
                f=1;
                break;
            }
        }

        ll c=0;
        if(f==1)
        {
            for(i=0;i<=n;i++)
            {
                if(b[i]==x&&c==0)
                    c=1;
                else
                    printf("%lld ",b[i]);
            }
            nl;
        }
        else
        {
            s-=b[n];
            if(s==b[n])
            {
                for(i=0;i<n;i++)
                    printf("%lld ",b[i]);
                    nl;
            }
            else
                printf("-1\n");
        }
    }
    //cout << s2 <<"\n";
    return 0;
}