B. Phoenix and Beauty

B. Phoenix and Beauty

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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

Phoenix currently has an array aa of length nn. He wants to insert some number of integers, possibly zero, into his array such that it becomes beautiful. The inserted integers must be between 11 and nn 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 tt (1≤t≤501≤t≤50) — the number of test cases.

The first line of each test case contains two integers nn and kk (1≤k≤n≤1001≤k≤n≤100).

The second line of each test case contains nn space-separated integers (1≤ai≤n1≤ai≤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 mm (n≤m≤104n≤m≤104). You don't need to minimize mm.

The second line should contain mm space-separated integers (1≤bi≤n1≤bi≤n) — a beautiful array that Phoenix can obtain after inserting some, possibly zero, integers into his array aa. You may print integers that weren't originally in array aa.

If there are multiple solutions, print any. It's guaranteed that if we can make array aa beautiful, we can always make it with resulting length no more than 104104.

Example

input

Copy

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

Copy

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 aa beautiful by inserting the integer 11 at index 33 (in between the two existing 22s). Now, all subarrays of length k=2k=2 have the same sum 33. There exists many other possible solutions, for example:

• 2,1,2,1,2,12,1,2,1,2,1
• 1,2,1,2,1,21,2,1,2,1,2

In the second test case, the array is already beautiful: all subarrays of length k=3k=3 have the same sum 55.

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

In the fourth test case, the array bb shown is beautiful and all subarrays of length k=4k=4 have the same sum 1010. There exist other solutions also.

=========================================================================

首先发现要想任意k段合都是相等的，必须是1234k1234k1234k这种排列

而题目并不要求长度最小，所以我们可以把整个数组都给放进去（去重）进行n次，这样就保证了每个段都包含原数组一个元素,n个段就构成了原数列。

无解的情况是一个段超过了k种元素

# include
# include
 
using namespace std;
 
int main ()
{
    int t;
    cin>>t;
 
    while(t--)
    {
        int n,k;
 
        cin>>n>>k;
 
        set<int>s;
        for(int i=1;i<=n;i++)
        {
            int x;
            cin>>x;
 
            s.insert(x);
        }
 
        if(s.size()>k)
        {
            cout<<-1<
        }
        else
        {
            cout<
 
            for(int i=1;i<=n;i++)
            {
                int cnt=0;
 
                for(auto it:s)
                {
                    cout<" ";
                    cnt++;
                }
 
                while(cnt
                {
                    cout<" ";
                    cnt++;
                }
 
            }
 
            cout<
 
        }
    }
 
    return 0;
 
}