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 Solution {
    public static void main(String[] args) {

        try {
            FastScanner in = new FastScanner(System.in);
            PrintWriter out = new PrintWriter(System.out);

            int T = in.nextInt();
            for (int i = 0; i < T; i++) {
                int n = in.nextInt();
                long k = in.nextLong();
                Long[] array = new Long[n];
                for (int j = 0; j < n; j++) {
                    array[j] = in.nextLong();
                }
                String s = isPossible(array, n, k) ? "YES" : "NO";
                out.println(s);
            }
            out.close();

        } catch(Exception exc) {
            throw new RuntimeException(exc);
        }
    }

    private static boolean isPossible(Long[] array, int n, long k) {
        if (k == 1L)
            return true;

        Arrays.sort(array);
        String[] logArray = new String[n];
        HashSet<Integer> taken = new HashSet<>();
        int next;
        long j;
        int p;
        StringBuilder sb;
        for (int i = 0; i < array.length; i++) {
            sb = new StringBuilder();
            j = array[i];
            p = 0;
            if (j == 0) {
                logArray[i] = "0";
            }
            else {
                while (j > 0) {
                    long remainder = j % k;
                    if (remainder != 0 && remainder != 1) {
                        return false;
                    }
                    if (remainder == 1) {
                        if (taken.contains(p)) {
                            return false;
                        }
                        taken.add(p);
                    }
                    sb.append(remainder);
                    j /= k;
                    p++;
                }
                logArray[i] = sb.toString();
            }
//            if (i > 0) {
//                for (int l = 0; l < logArray[i - 1].length(); l++) {
//                    if (logArray[i - 1].charAt(l) != logArray[i].charAt(l))
//                        return false;
//                }
//            }
        }
        return true;
    }

    //@
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream i) {
            br = new BufferedReader(new InputStreamReader(i));
            st = new StringTokenizer("");
        }

        public String next() throws IOException {
            if(st.hasMoreTokens())
                return st.nextToken();
            else
                st = new StringTokenizer(br.readLine());
            return next();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        //#
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        //$
    }
}
