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.util.*;
import java.lang.*;
import java.io.*;
import java.text.*;

/* Name of the class has to be "Main" only if the class is public*/
public class CF1312C
{
    static 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;
        }
    }
    
    static class Node {
        
        long pp;
        long a, b;
        
        Node(long x, long y) {
            a = x;
            b = y;
            pp = a * b;
        }
    }
    static class Comp implements Comparator<Node> {
        
        public int compare(Node o1, Node o2) {
            if (o1.pp > o2.pp) {
                return 1;
            } else {
                return -1;
            }
        }
    }
    public static void main(String[] args) {
        FastReader sc=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        //your code starts here
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
            int k=sc.nextInt();
            long a[]=new long[n];
            long max=-1;
            for(int i =0;i<n;i++)
            {
                a[i]=sc.nextLong();
                if(max<a[i]) max=a[i];
            }
            int ctr=0;
            while(max>0)
            {
                ++ctr; max/=k;
            }
            long pow[][]=new long[n][ctr];
            int flag=1;
            for(int i=0;i<n;i++)
            {
                long s=a[i]; int pos=ctr-1;
                while(s>0) {
                    long d=s%k;
                    if(d==0 || d==1)
                    {
                        pow[i][pos]=d; --pos;
                        s/=k;
                    }
                    else {
                        flag=0; break;
                    }
                }
            }
            for(int i=0;i<ctr;i++)
            {
                int res=0;
                for(int j=0;j<n;j++)
                    res+=pow[j][i];
                if(res>1){
                    flag=0; break;
                }
            }
            if(flag==0) out.println("NO");
            else out.println("YES");
        }
        out.close();
    }
}
