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:
#include <bits/stdc++.h>
#include <algorithm>
#include <cmath>
#include <map>
#include <vector>
#include <stack>
using namespace std;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<pair<ll, ll>> vpl;
typedef map<ll, ll> mll;
#define ff(i, c, n) for (ll i = c; i < n; i++)
#define fb(i, c, n) for (ll i = c; i >= n; --i)
#define forn(i, n) for (int i = 0; i < int(n); i++)
#define max(a, b) ((a > b) ? a : b)
#define min(a, b) ((a > b) ? b : a)
#define pb push_back
#define mp make_pair
#define inp(n) \
    ll n;      \
    cin >> n;
#define ina(a, n) \
    ll a[n];      \
    ff(i, 0, n) cin >> a[i];
#define inm(a, n, m)                    \
    ff(i, 0, n)                         \
    {                                   \
        ff(j, 0, m) { cin >> a[i][j]; } \
    }
#define ins(s) \
    string s;  \
    cin >> s;
#define out(n) cout << n << "\n";
#define outv(v)           \
    for (auto x : v)      \
    {                     \
        cout << x << " "; \
    }                     \
    cout << "\n";
#define outm(mp)                                    \
    for (auto x : mp)                               \
    {                                               \
        cout << x.first << " " << x.second << endl; \
    }
#define outa(a, n)              \
    for (int i = 0; i < n; i++) \
    {                           \
        cout << a[i] << " ";    \
    }                           \
    cout << endl;
#define gcd(m, n) __gcd(m, n)
#define testcase \
    inp(t);      \
    while (t--)  \
    {            \
        solve(); \
    }
#define MODINF 1000000007
#define all(v) (v).begin(), (v).end()

ll fact[1000001] = {0};

//fucntion to precalculate factorials and store them in an array
void preFact()
{
    fact[0] = 1;
    fact[1] = 1;
    ff(i, 2, 1000001)
    {
        fact[i] = (fact[i - 1] * (i % MODINF)) % MODINF;
    }
}

//fucntion to check if a number is prime or not
bool isPrime(int n)
{
    if (n <= 1)
        return false;
    if (n <= 3)
        return true;
    if (n % 2 == 0 || n % 3 == 0)
        return false;
    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
    return true;
}

//function to get the greatest set bit of a number
ll setBitNumber(ll n)
{
    if (n == 0)
        return 0;

    ll msb = 0;
    n = n / 2;
    while (n != 0)
    {
        n = n / 2;
        msb++;
    }

    return (msb);
}

//function to calculate a^n in O(logn)
ll binaryExpon(ll a, ll b)
{
    ll ans = 1;
    while (b > 0)
    {
        if (b % 2 == 1)
        {
            ans *= (a % MODINF) % MODINF;
            ans = ans % MODINF;
        }
        a *= (a % MODINF) % MODINF;
        a = a % MODINF;
        b = b >> 1;
    }
    return ans % MODINF;
}

//function to calculate nCr using modular inverse
ll nCr(ll n, ll r)
{
    if (n < r)
    {
        return 0;
    }
    else
    {
        ll ans = fact[n];
        ans = ans * (binaryExpon(fact[r], (MODINF - 2)) % MODINF) % MODINF;
        ans = ans * (binaryExpon(fact[n - r], (MODINF - 2)) % MODINF) % MODINF;
        return ans;
    }
}

ll gcd(ll a, ll b)
{
    if (b == 0)
    {
        return a;
    }
    return gcd(a % b, b);
}

ll check(string s, ll n)
{
    ff(i, 0, n / 2)
    {

        if (s[i] != s[n - i - 1])
        {
            return 0;
        }
    }
    return 1;
}

pair<ll, ll> Search(char ch, ll l, ll r, string t)
{
    ff(i, l, r)
    {
        if (t[i] == ch)
        {
            return {1, i};
        }
    }
    return {0, -1};
}

void solve()
{
    inp(n);
    ina(b, n + 2);
    sort(b, b + n + 2);
    vl a;
    ll x;
    ll sumb = 0;
    set<ll> s;
    ff(i, 0, n + 2)
    {
        s.insert(b[i]);
        sumb += b[i];
    }

    ll tempsum = 0;
    ll checksum = 0;
    ff(i, 0, n + 2)
    {
        x = b[i];
        if ((sumb - x) % 2 == 1)
        {
            continue;
        }
        else
        {
            tempsum = (sumb - x) / 2;
            if (s.find(tempsum) != s.end())
            {
                ll c = 0;
                checksum = tempsum;
                ff(j, 0, n + 2)
                {
                    if (i == j || (b[j] == tempsum && c == 0))
                    {
                        if (i == j && c == 0)
                        {
                            c = 0;
                        }
                        else
                        {
                            c = 1;
                        }
                        continue;
                    }
                    a.push_back(b[j]);
                }
                break;
            }
        }
    }

    if (a.size() == 0)
    {
        out(-1) return;
    }
    else
    {
        ff(i, 0, n)
        {
            checksum -= a[i];
        }
        if (checksum != 0)
        {
            out(-1) return;
        }
        outv(a) return;
    }
}

int main()
{
#ifndef ONLINE_JUDGE
    if (fopen("input.txt", "r"))
    {
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    }
#endif
    ios_base::sync_with_stdio(false);
    srand(chrono::high_resolution_clock::now().time_since_epoch().count());
    cin.tie(0);
    cout.tie(0);
    // solve();
    testcase
}