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.Scanner;

/**

@author liuwp2

@version 0.1

@description

@date 2021/2/20 */
public class week
{
    public static void main(String args[])
    {
        Long[][] poww=new Long[40][64];
        Scanner scan = new Scanner(System.in);
        int t=scan.nextInt();
        while ((t--)>0)
        {
            int n = scan.nextInt();
            int k = scan.nextInt();
            for(int i=0; i<=39; i++)
            {
                for (int j = 0; j<=63; j++) 
                    poww[i][j] = Long.valueOf(0);
            }
            for(int i=1; i<=n; i++)
            {
                int cnt=0;
                long x=scan.nextLong();
                while (x>0)
                {
                    poww[i][cnt++]=x%k;
                    x/=k;
                }
            }
            int flag=1;
            for(int i=0; i<=63; i++)
            {
                long sum=0;
                for(int j=1; j<=n; j++)
                {
                    sum+=poww[j][i];
                }
               if(sum>1)
                   flag=0;              
            }
             if(flag==1)
                System.out.print("YES\n");

             else
                System.out.print("NO\n");     
        }
//scan.close();
    }

}

			 	 	 	   		  			  	 		   		