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 codeforces {

    public static long power(int a,int b){
        if(a==0 || b==0)
        return 1;
        long ans=power(a,b/2);
        ans*=ans;
        if(b%2==1)
        ans*=a;
        return ans;
    }

    public static boolean bata(long[] a,int n,int k,HashSet<Integer> hs){
        for(long x:a){
            while(x!=0){
                int power=-1;
                long raised=1;
                while(raised<=x){
                    raised*=k;
                    power++;
                }
                if(hs.contains(power))
                return false;
                hs.add(power);
                // System.out.println(raised);
                x=x-raised/k;
            }            
        }
        return true;
    }

    public static long max(long a,long b){
        return Math.max(a,b);
    }
    public static void main(String args[] ) throws Exception {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder str=new StringBuilder();
        PrintWriter out=new PrintWriter(System.out);
        String[] l;
        HashSet<Integer> hs;
        long[] a;
        // out.println(power(2,3));
        int t=Integer.parseInt(br.readLine());
        while(t-->0){
            l=br.readLine().split(" ");
            int n=Integer.parseInt(l[0]),k=Integer.parseInt(l[1]);
            hs=new HashSet<>();
            a=new long[n];
            l=br.readLine().split(" ");
            for(int i=0;i<n;i++)
                a[i]=Long.parseLong(l[i]);
            boolean solve=bata(a,n,k,hs);
            str.append((solve)?"YES\n":"NO\n");
        }
        out.print(str);
        out.close();
   }
}

