Suppose you are performing the following algorithm. There is an array v_1, v_2, ..., v_n filled with zeroes at start. The following operation is applied to the array several times — at i-th step (0-indexed) you can: 

  * either choose position pos (1 ≤ pos ≤ n) and increase v_{pos} by k^i; 
  * or not choose any position and skip this step. 



You can choose how the algorithm would behave on each step and when to stop it. The question is: can you make array v equal to the given array a (v_j = a_j for each j) after some step?

Input

The first line contains one integer T (1 ≤ T ≤ 1000) — the number of test cases. Next 2T lines contain test cases — two lines per test case.

The first line of each test case contains two integers n and k (1 ≤ n ≤ 30, 2 ≤ k ≤ 100) — the size of arrays v and a and value k used in the algorithm.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^{16}) — the array you'd like to achieve.

Output

For each test case print YES (case insensitive) if you can achieve the array a after some step or NO (case insensitive) otherwise.

Example

Input


5
4 100
0 0 0 0
1 2
1
3 4
1 4 1
3 2
0 1 3
3 9
0 59049 810


Output


YES
YES
NO
NO
YES

Note

In the first test case, you can stop the algorithm before the 0-th step, or don't choose any position several times and stop the algorithm.

In the second test case, you can add k^0 to v_1 and stop the algorithm.

In the third test case, you can't make two 1 in the array v.

In the fifth test case, you can skip 9^0 and 9^1, then add 9^2 and 9^3 to v_3, skip 9^4 and finally, add 9^5 to v_2.
import javax.swing.*;
import java.io.*;
import java.util.*;
import java.math.*;

import static java.util.Comparator.*;


public class Codeforces {

    static List<Integer> check(long n,long val)
    {
        List<Integer> list=new ArrayList<>();
        int i=0;
        while(val>0)
        {
            while((long)Math.pow(n,i)<=val)
            {
                i++;
            }

            i--;
            list.add(i);
            val-=(long)Math.pow(n,i);
//            System.out.println(val+" "+i);
            i=0;
//            if(val<0)

        }
        return list;

    }
    public static void main(String[] args) throws IOException {
        FastReader s = new FastReader();
        int t=s.nextInt();
        for(int i=0;i<t;i++)
        {
            int n=s.nextInt();
            long k=s.nextInt();
            long[] arr=new long[n];
            for(int j=0;j<n;j++)
            {
                arr[j]=s.nextLong();
            }

            HashSet<Integer> set=new HashSet<>();
            int f=0;
            for(int j=0;j<n;j++)
            {
                int flag=0;
                if(arr[j]==0)
                {
                    continue;
                }
                List<Integer> list=check(k,arr[j]);
//                System.out.println(arr[j]);
//                for(int l:list)
//                {
//                    System.out.print(l+" ");
//                }
//                System.out.println();
                for(int l:list)
                {
                    if(set.contains(l))
                    {
                        flag=1;
                        break;
                    }
                    else {
                        set.add(l);
                    }
                }
                if(flag==1)
                {
                    f=1;
                    break;
                }
            }
            if(f==1)
            {
                System.out.println("NO");
            }
            else {
                System.out.println("YES");
            }
        }


    }
}

class FastReader
{
    BufferedReader br;
    StringTokenizer st;

    public FastReader()
    {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }

    String next()
    {
        while (st == null || !st.hasMoreElements())
        {
            try
            {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException  e)
            {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt()
    {
        return Integer.parseInt(next());
    }

    long nextLong()
    {
        return Long.parseLong(next());
    }

    double nextDouble()
    {
        return Double.parseDouble(next());
    }

    String nextLine()
    {
        String str = "";
        try
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}
