Phoenix loves beautiful arrays. An array is beautiful if all its subarrays of length $k$ have the same sum. A subarray of an array is any sequence of consecutive elements.

Phoenix currently has an array $a$ of length $n$. He wants to insert some number of integers, possibly zero, into his array such that it becomes beautiful. The inserted integers must be between $1$ and $n$ inclusive. Integers may be inserted anywhere (even before the first or after the last element), and he is not trying to minimize the number of inserted integers.


-----Input-----

The input consists of multiple test cases. The first line contains an integer $t$ ($1 \le t \le 50$) — the number of test cases.

The first line of each test case contains two integers $n$ and $k$ ($1 \le k \le n \le 100$).

The second line of each test case contains $n$ space-separated integers ($1 \le a_i \le n$) — the array that Phoenix currently has. This array may or may not be already beautiful.


-----Output-----

For each test case, if it is impossible to create a beautiful array, print -1. Otherwise, print two lines.

The first line should contain the length of the beautiful array $m$ ($n \le m \le 10^4$). You don't need to minimize $m$.

The second line should contain $m$ space-separated integers ($1 \le b_i \le n$) — a beautiful array that Phoenix can obtain after inserting some, possibly zero, integers into his array $a$. You may print integers that weren't originally in array $a$.

If there are multiple solutions, print any. It's guaranteed that if we can make array $a$ beautiful, we can always make it with resulting length no more than $10^4$.


-----Example-----
Input
4
4 2
1 2 2 1
4 3
1 2 2 1
3 2
1 2 3
4 4
4 3 4 2

Output
5
1 2 1 2 1
4
1 2 2 1
-1
7
4 3 2 1 4 3 2


-----Note-----

In the first test case, we can make array $a$ beautiful by inserting the integer $1$ at index $3$ (in between the two existing $2$s). Now, all subarrays of length $k=2$ have the same sum $3$. There exists many other possible solutions, for example:   $2, 1, 2, 1, 2, 1$  $1, 2, 1, 2, 1, 2$ 

In the second test case, the array is already beautiful: all subarrays of length $k=3$ have the same sum $5$.

In the third test case, it can be shown that we cannot insert numbers to make array $a$ beautiful.

In the fourth test case, the array $b$ shown is beautiful and all subarrays of length $k=4$ have the same sum $10$. There exist other solutions also.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from collections import Counter\n\ndef read_int():\n    return int(input())\n\n\ndef read_ints():\n    return map(int, input().split(' '))\n\n\nt = read_int()\nfor case_num in range(t):\n    n, k = read_ints()\n    a = list(read_ints())\n    cnt = Counter(a)\n    distinct = len(cnt)\n    if distinct > k:\n        print(-1)\n    else:\n        print(n * k)\n        s = set(cnt)\n        for i in range(1, n + 1):\n            if len(s) < k and not i in s:\n                s.add(i)\n        ans = list(s) * n\n        print(' '.join(map(str, ans)))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14299