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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;

public class problem3 {
    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int T = Integer.parseInt(reader.readLine());
        for (int i = 0; i < T; i++) {
            StringTokenizer tokenizer = new StringTokenizer(reader.readLine());
            int n = Integer.parseInt(tokenizer.nextToken());
            long k = Long.parseLong(tokenizer.nextToken());
            long[] a = new long[n];
            tokenizer = new StringTokenizer(reader.readLine());
            for (int j = 0; j < n; j++) {
                a[j] = Long.parseLong(tokenizer.nextToken());
            }
            HashSet<Integer> set = new HashSet<>();
            boolean flag = true;
            ArrayList<Long> list = new ArrayList<>();
            for (int j = 0; j < n && flag; j++) {
                long div = a[j];
                while (div != 0){
                    long mod = div % k;
                    div = div/k;
                    if(mod > 1){
                        flag = false;
                        break;
                    }
                    list.add(mod);
                }
                for (int s = 0; s < list.size(); s++) {
                    if(list.get(s) == 1 && set.contains(s)){
                        flag = false;
                        break;
                    }else if(list.get(s) == 1){
                        set.add(s);
                    }
                }
                list.clear();
            }
            System.out.println(flag ? "YES" : "NO");

        }
    }
}
