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.*;

public class Main {
    public static void main(String[] args){
        Scanner scanner = new Scanner(System.in);
        int size = scanner.nextInt();
        long[] mas;
        long max = 0, now;
        boolean flag;
        LinkedList<Long> kk = new LinkedList<>();
        for(int i = 0, k, s; i < size; i++, max = 0){
            flag = true;
            kk.add(1L);
            s = scanner.nextInt();
            k = scanner.nextInt();
            mas = new long[s];
            for(int j = 0; j < s; j++){
                mas[j] = scanner.nextLong();
                max = Math.max(mas[j], max);
            }
            Arrays.sort(mas);
            while (kk.get(kk.size() - 1) < max){
                kk.add(kk.get(kk.size() - 1) * k);
            }
            for(int q = mas.length - 1; q >= 0; q--) {
                Iterator<Long> it = kk.descendingIterator();
                while (it.hasNext()){
                    now = it.next();
                    if(now <= mas[q]){
                        mas[q] -= now;
                        it.remove();
                    }
                }
                if(mas[q] != 0){
                    System.out.println("NO");
                    flag = false;
                    break;
                }
            }
            if(flag) {
                System.out.println("YES");
            }
            kk.clear();
        }
    }
}