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 java.io.*;
import java.util.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        int t=Integer.parseInt(br.readLine());
        for(int x=0;x<t;x++)
        {
            String str[]=br.readLine().split(" ");
            int n=Integer.parseInt(str[0]);
            int k=Integer.parseInt(str[1]);
            str=br.readLine().split(" ");
            long arr[]=new long[n];
            for(int i=0;i<n;i++)
            arr[i]=Long.parseLong(str[i]);
            Arrays.sort(arr);
            /*ArrayList<Long> pow=new ArrayList<>();
            for(int i=0;i<n;i++)
            {
                if((long)Math.pow(k,i)>(long)Math.pow(10,16))
                break;
                pow.add((long)Math.pow(k,i));
            }*/
            boolean vis[]=new boolean[64];
            boolean imp=false;
            outer:for(int i=0;i<n;i++)
            {
                if(arr[i]>0)
                {
                    int cntr=0;
                    long temp=arr[i];
                    //StringBuffer sb=new StringBuffer();
                    while(temp>0)
                    {
                        //long r=temp%k;
                        temp/=k;
                        cntr++;
                    }
                    temp=arr[i];
                    /*String s=new String(sb);
                    for(int j=s.length()-1;j>=0;j--)
                    {
                        if((s.charAt(j)-'0')>0&&!vis[s.length()-1-j])
                        {
                            vis[s.length()-1-j]=true;
                        }
                        else if((s.charAt(j)-'0')>0&&vis[s.length()-1-j])
                        {
                            imp=true;
                            break outer;
                        }
                    }*/
                    for(int j=cntr;j>=0;j--)
                    {
                        long num=(long)Math.pow(k,j);
                        if(temp>=num)
                        {
                            if(!vis[j])
                            {
                                temp-=num;
                                vis[j]=true;
                            }
                            else
                            break;
                        }
                    }
                    if(temp!=0)
                    {
                        imp=true;
                        break;
                    }
                }
            }
            if(imp)
            pw.println("NO");
            else
            pw.println("YES");
        }
        pw.flush();
        pw.close();
    }
}