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.*;
public class Main{
    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());
        }
        String nextLine(){
            String sr = "";
            try{
                sr = br.readLine();
            }
            catch(IOException e){
                e.printStackTrace();
            }
            return sr;
        }
    }
    public static void main(String args[]) throws Exception{
        FastReader ft = new FastReader();
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int t = ft.nextInt();
        while(t-->0){
            int n = ft.nextInt();
            int k = ft.nextInt();
            int o = 0;
            long a[] = new long[n];
            for(int i = 0;i<n;i++){
                a[i] = ft.nextLong();
            }
            int arr[]=new int[100];
			for(int i=0;i<n;i++){
				int j=0;
				while(a[i]>0){
					arr[j++]+=(int)(a[i]%k);
					a[i]/=k;
				}
			}
			for(int i=0;i<100;i++){
				if(arr[i]>1){
					o=1;break;
				}
			}
            if(o == 0)
            out.write("YES\n");
            else
            out.write("NO\n");
        }
        out.flush();}}