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.*;
 
 public class Solution {
  // static int dp[][]=new int[10001][10001];
     static ArrayList<Integer> graph[];
     static int diff[];
     static int dp[];
     static ArrayList<Integer> newgraph[];
     static int parent[];
     static boolean vis[];
     static int k;
     static int seive[]=new int[1000001];
     static int dis[]=new int[1000001];
     static int subtree[]=new int[1000001];
     static int N =1000001;
     static HashSet<String> hm=new HashSet<>();
     static HashSet<String> hm1=new HashSet<>();
     static HashMap<Integer, Character> hash=new HashMap<>();
     static Stack<Integer> st=new Stack<>();
     static int time=0;
     static int components=0;
     public static void main(String[] args) {
       Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
       StringBuilder sb=new StringBuilder();
      int t=sc.nextInt();
      while(t-->0)
      {
        int n=sc.nextInt();
        int k=sc.nextInt();
        long sum=0;
        PriorityQueue<Long> pq=new PriorityQueue<>(Collections.reverseOrder());
        long a[]=new long[n];
        for( int i=0;i<n;i++)
        {
        a[i]=sc.nextLong();
        sum+=a[i];
        if(a[i]!=0)
        pq.add(a[i]);
        }
        int i=0;
        while(Math.pow(k,i)<=sum)
        {
          i++;
        }
        for( int j=i;j>=0;j--)
        {
          if(!pq.isEmpty()&&(long)Math.pow(k,j)<=pq.peek())
          {
            long val=pq.remove();
            val-=(long)Math.pow(k,j);
            if(val==0)
            {
 
            }
            else
            {
              pq.add(val);
            }
          }
        }
        if(pq.size()==0)
        {
          sb.append("YES\n");
        }
        else
        sb.append("NO\n");
      }
        System.out.println(sb.toString());
 
}
}
 
class Pair
{
long x,y;
Pair(long x, long y)
{
this.x=x;
this.y=y;
}
}
class myComparator implements Comparator<Pair>
{
public int compare(Pair a, Pair b)
{
return Long.compare(b.y, a.y);
}
}