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.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) {
        
        FastScanner sc = new FastScanner(System.in);
        
        int T = Integer.parseInt(sc.next());
        StringBuilder sb = new StringBuilder();
        for(int t = 0; t < T; t++){
            int n = Integer.parseInt(sc.next());
            long k = Long.parseLong(sc.next());
            long[] b = new long[55];
            b[0] = 1;
            for(int i = 1; i < 55; i++){
                if(b[i-1] >= 10_000_000_000_000_000L){
                    b[i] = Long.MAX_VALUE;
                }else{
                    b[i] = b[i-1] * k;
                }
            }
            Set<Integer> set = new HashSet<>();
            
            boolean flag = true;
            for(int i = 0; i < n; i++){
                long a = Long.parseLong(sc.next());
                for(int j = 54; j >= 0; j--){
                    if(a >= b[j]){
                        a -= b[j];
                        if(!set.add(j)) flag = false;
                    }
                }
                if(a != 0) flag = false;
            }
            sb.append(flag ? "YES" : "NO").append(System.lineSeparator());
        }
        System.out.print(sb);
    }
    
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }
        String next(){
            while(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException  e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
    }
}