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.
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

public class GFG {
	public static void main (String[] args) {
	   Scanner sc = new Scanner(System.in);
	   int t = sc.nextInt();
	   while(t-- > 0) {
	       int n = sc.nextInt(), k = sc.nextInt();
	       long[] a = new long[n];
	       for(int i = 0;i < n;i++) {
	           a[i] = sc.nextLong();
	       }
	       
	       List<Long> d = new ArrayList<>();
	       int i = 0;
	       while((long)Math.pow(k, i) <= (long)Math.pow(10, 16)) {
	          d.add((long)Math.pow(k, i++));
	       }
	       
	       Set<Integer> h = new HashSet<>();
	       boolean flag = true;
	       for(long x : a) {
	           if(x == 0) continue;
	           while(flag) {
	               int j = 0;
	               for(i = 0;i < d.size();i++) {
	                   if(x >= d.get(i)) {
	                       j = i;
	                   }else{
	                       break;
	                   }
	               }
	               if(h.contains(j)) {
	                   flag = false;
	                   break;
	               }
	               h.add(j);
	               x = x - d.get(j);
	              if(x == 0) break;
	         }
	     }
	     if(flag) {
	         System.out.println("YES");
	     }else{
	       System.out.println("NO");
	     }
	   }
	}
}