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.ArrayList;
import java.util.Collections;
import java.util.LinkedList;
import java.util.Scanner;

public class AddingPowers {

    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        int t = scan.nextInt();
        while (t-- > 0) {
            int n = scan.nextInt();
            int m = scan.nextInt();
            long mx = 0;

            ArrayList<Long> arra = new ArrayList<Long>();
            for (int i = 0; i < n; i++) {
                long in = scan.nextLong();

                if (in != 0) {
                    arra.add(in);
                }
                mx = Math.max(mx, in);

            }

            Collections.sort(arra);
            LinkedList<Long> p = new LinkedList<Long>();
            int j = 0;
            while (Math.pow(m, j) <= mx) {
                p.add((long) Math.pow(m, j));
                ++j;
            }
            Collections.sort(p, Collections.reverseOrder());

            int e = arra.size();
            boolean b = false;
            int res = 0;
            for (int i = 0; i < e; i++) {
                long s = 0;
                j = 0;
                while (true) {
                    try {
                        if (s + p.get(j) > arra.get(i)) {
                            ++j;
                        } else if (s == arra.get(i)) {
                            ++j;
                            p.remove(p.get(j));
                            break;
                        } else if (s + p.get(j) <= arra.get(i)) {

                            s += p.get(j);
                            p.remove(p.get(j));

                            if (s == arra.get(i)) {
                                ++res;
                                break;

                            }

                        }
                    } catch (Exception q) {
                        b = true;
                        break;
                    }

                }
                if (b) {
                    break;
                }
            }
            if (res == e) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }

        }
    }

}
