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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
public class cdfer83b
{
	static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }
	static long power(long x, long y) 
	{ 
	    long temp; 
	    if( y == 0) 
	        return 1; 
	    temp = power(x, y/2); 
	    if (y%2 == 0) 
	        return temp*temp; 
	    else
	        return x*temp*temp; 
	}
	public static void main(String args[])throws Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		for(int i=0;i<t;i++)
		{
			String s=br.readLine();
			String str[]=s.split(" ");
			int n=Integer.parseInt(str[0]);
			int k=Integer.parseInt(str[1]);
			s=br.readLine();
			String ss[]=s.split(" ");
			long arr[]=new long[n];
			for(int j=0;j<n;j++)
			arr[j]=Long.parseLong(ss[j]);
			Arrays.sort(arr);
			int j;
			for(j=0;;j++)
			{
				if(power(k,j)>=arr[n-1])
					break;
			}
			int tempo[]=new int[j+1];
			//System.out.println(j);
			int f=0;
			for(;j>=0;j--)
			{
				if(arr[n-1]==0)
				{
					f=0;
					break;
				}
				if(arr[n-1]>=power(k,j)&&j!=0&&tempo[j]==1)
				{
					f=1;
					break;
				}
				if(arr[n-1]>=power(k,j))
				{
					tempo[j]=1;
					arr[n-1]=arr[n-1]-power(k,j);
					Arrays.sort(arr);
				}
			}
			if(f==0&&arr[n-1]==0)
//			{
//				for(int kk=0;kk<n;kk++)
//					System.out.print(arr[kk]+" ");
//				System.out.println();
				System.out.println("YES");
			else
			System.out.println("NO");
		}
	}

}
