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.lang.*;

public class MyClass {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        
        int cases = scan.nextInt();
        while(cases>0){
            int n = scan.nextInt(); int k = scan.nextInt(); long max = 0;
            
            List<Long> used = new ArrayList<Long>();
            long[] v = new long[n];
            
            //input 
            for(int i = 0; i<n; i++){
                v[i]= scan.nextLong();
            }
            Arrays.sort(v); 
            int temp = 0;
            //find max i
            while(max<v[n-1]){
                temp++;
                max=(long)Math.pow(k,temp);
            }
            
            
            
            
            for(int i = 0; i<=temp; i++){
                used.add((long)Math.pow(k,i));
            }
            
            for(int i = 0; i<used.size(); i++){
                //System.out.print(used.get(i)+" ");
            }
            
            
            int index = n-1;
            //System.out.println(n);
                while(index>=0){
                    for(int i=used.size()-1; i>=0; i--){
                        if(used.get(i)<= v[index]){
                            v[index]-=used.get(i);
                            used.remove(i);
                        }
                    }
                    index--;
                }
    
           // System.out.println();
    
            for(int i = 0; i<n; i++){
               // System.out.print(v[i]+" ");
            }
            
            boolean yes = true;
            for(int i = 0; i<n; i++){
                if(v[i]!=0){
                    yes = false;
                    break;
                }
            }
            if(yes){
                System.out.println("YES");
            }else{
                System.out.println("NO");
            }
            
            
            cases--;
        }
    }
}