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.*; 
import java.util.*; 
public class Main {
    public static void main(String args[]) throws IOException {
        Scanner input=new Scanner(System.in);
        int test=input.nextInt();
        for(int t=1;t<=test;t++) {
            int n=input.nextInt();
            int k=input.nextInt();
            ArrayList<Long> pow_lis=new ArrayList<>();
            long pow=1;
            for(int i=0;pow>0;i++) {
                pow_lis.add(pow);
                pow*=k;
            }
            boolean is_pos=true;
            for(int i=0;i<n;i++) {
                if(solve(input.nextLong(),pow_lis)!=0) {
                    is_pos=false;
                } 
            }
            if(is_pos) {
                System.out.println("YES");
            }
            else {
                System.out.println("NO");
            }
        }
    }
    public static long solve(long n,ArrayList<Long> pow_lis) {
        for(int i=pow_lis.size()-1;i>=0;i--) {
            if(pow_lis.get(i)<=n) {
                n-=pow_lis.get(i);
                pow_lis.remove(i);
            }
        }
        return n;
    }
}
