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.io.*;

public class AddingPowers {

	// https://codeforces.com/problemset/problem/1312/C
		
	public static void main(String[] args) throws IOException, FileNotFoundException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		//BufferedReader in = new BufferedReader(new FileReader("AddingPowers"));

		int t = Integer.parseInt(in.readLine());  
		for (int j = 0; j < t; j++) {
			StringTokenizer st = new StringTokenizer(in.readLine());
			int n = Integer.parseInt(st.nextToken()); 
			int k = Integer.parseInt(st.nextToken()); 
			HashSet<Long> a = new HashSet<>();
			long[] arr = new long[n];
			st = new StringTokenizer(in.readLine());
			boolean works = true;
			outerloop: for (int i = 0 ; i < n; i++) {
				arr[i] = Long.parseLong(st.nextToken());
				// for each one check
				if (arr[i] == 0) continue;
				else {
					ArrayList<Long> cur = new ArrayList<>();
					while (arr[i] > 0) {
						if (arr[i] % k > 1) {
							works = false;
							break;
						}
						else {
							cur.add(arr[i] % k);
							arr[i] /= k;
						}
					}
					long p = 0;
					for (int m = 0; m < cur.size(); ++m) {
						if (cur.get(m) != 0) {
							if (a.contains((long) (cur.get(m) * Math.pow(k, p)))) {
								works = false;
								break outerloop;
							}
							else {
								a.add((long) (cur.get(m) * Math.pow(k, p)));
							}
						}
						p++;
					}
				}
			}
			
			if (works) System.out.println("YES");
			else System.out.println("NO");
			
		}
	}
}
