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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.*;
 
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(32768, in, out);
        out.close();
    }
 
static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        
 
    }
static class TaskD{
        boolean flag_g = true;
        String check(int m,long n){
            String ans = "";
            long  t = n;
            while(t >0){
                ans+= t%m;
                if(t%m > 1) flag_g = false;
                t/=m;
                
            }
            return ans;
        }
        String addZeroes(String inp,int till){
            String op =inp;
            for(int i=0;i<till-inp.length();i++){
                op+="0";
            }
            return op;
        }
        public void solve(int testNum,InputReader in,PrintWriter out){
          int t  = in.nextInt();
          while(t-->0){
              int n = in.nextInt();
              int k = in.nextInt();
              ArrayList<String>lists = new ArrayList<>();
              boolean ans = true;
              int max = 0;
              for(int i=0;i<n;i++){
                  long x = in.nextLong();
                  lists.add(check(k,x));
                  max = Math.max(max,check(k,x).length());
              }
              for(int i=0;i<n;i++){
                  lists.set(i,addZeroes(lists.get(i),max));
              }
              
              for(int i=0;i<max;i++){
                  HashMap<Character,Boolean>hash = new HashMap<>();
                  for(int j=0;j<n;j++){
                      char ch = lists.get(j).charAt(i);
                      int x = ch - '0';
                      if((x>0 && hash.containsKey(ch)) || x>1){
                          ans = false;
                          break;
                      }
                      hash.put(lists.get(j).charAt(i),true);
                  }
                  if(!ans) break;
                  hash.clear();
              }
              
              if(ans && flag_g) out.println("YES");
              else out.println("NO");
              flag_g = true;
          }
        }
}
}