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.io.*;
import java.math.*;
public class EdC {

	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int t = Integer.parseInt(bf.readLine());
 		for(int i = 0;i<t;i++){
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
 			StringTokenizer st = new StringTokenizer(bf.readLine());
 			long a = Long.parseLong(st.nextToken());
 			int b = Integer.parseInt(st.nextToken());
 			StringTokenizer st1 = new StringTokenizer(bf.readLine());
 			ArrayList<Long> inputs= new ArrayList<Long>();
 			Set<Integer> used = new HashSet<Integer>();
 			for(int j=0;j<a;j++){
 				inputs.add(Long.parseLong(st1.nextToken()));
 			}
 			boolean found = true;
	 		for(int j = 0;j<a;j++){
	 			long temp = inputs.get(j);
	 			while(temp != 0){
		 			long y = 1;
		 			int count = 0;
		 			while (y <= temp){
		 				y*=b;
		 				count+=1;
		 			}
		 			y/=b;
		 			count-=1;
		 			if (used.contains(count)){
		 				found = false;
		 				break;
		 			}
		 			used.add(count);
		 			temp-=y;
	 			}
	 			if (found == false){
	 				break;
	 			}
	 		}
	 		if (found == false){
	 			out.println("NO");
	 		}
	 		else{
	 			out.println("YES");
	 		}
	 		
 		}
 		out.close();
 		
 		
 		
 	}
	public static long gcd(long a, long b) { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is

 		
 		
 		
 		
	


