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.lang.*;
import java.io.*;

//           THIS TEMPLATE MADE BY AKSH BANSAL.

public class Solution {
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    private static boolean[] isPrime;
    private static void primes(){
        int num = (int)1e6; // PRIMES FROM 1 TO NUM
        isPrime = new boolean[num];
     
        for (int i = 2; i< isPrime.length; i++) {
           isPrime[i] = true;
        }
        for (int i = 2; i< Math.sqrt(num); i++) {
           if(isPrime[i] == true) {
              for(int j = (i*i); j<num; j = j+i) {
                 isPrime[j] = false;
              }
           }
        }
    }
    private static long gcd(long a, long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }
    private static long pow(long x,long y){
        if(y==0)return 1;
        long temp = pow(x, y/2);
        if(y%2==1){
            return x*temp*temp;
        }
        else{
            return temp*temp;
        }
    }
    static ArrayList<Integer>[] adj;
    static void getAdj(int n,int q, FastReader sc){
        adj = new ArrayList[n+1];
        for(int i=1;i<=n;i++){
            adj[i] = new ArrayList<>();
        }
        for(int i=0;i<q;i++){
            int a = sc.nextInt();
            int b = sc.nextInt();

            adj[a].add(b);
            adj[b].add(a);
        }
    }
    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        primes();
        // ________________________________

        int t = sc.nextInt();
        StringBuilder output = new StringBuilder();

        while (t-- > 0) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            long[] arr =new long[n];
            for(int i=0;i<n;i++){
                arr[i] =sc.nextLong();
            }
            output.append(solver(arr, n, k)).append("\n");
            // solver(arr,n, out);
        }

        out.println(output);
        // _______________________________

        // int n = sc.nextInt();
        // out.println(solver());
        // ________________________________
        out.flush();
    }

    public static String solver(long[] arr, int n, int k) {
        //
        boolean allZero = true;
        for(int i=0;i<n;i++){
            if(arr[i]!=0){
                allZero = false;
            }
        }
        if(allZero)return "YES";

        boolean[][] ans = new boolean[n][65];
        for(int i=0;i<n;i++){
            long cur = arr[i];
            // String s = "";
            int count = 0;
            while(cur>0){
                long e = cur%k;
                if(e>1){
                    return "NO";
                }
                // s = String.valueOf(e)+s;
                ans[i][count] = e==1?true:false;
                cur = cur/k;
                count++;
            }
            // ans[i] = s;
        }

        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                for(int p = 0;p<65;p++){
                    if(ans[i][p] && ans[j][p]){
                        return "NO";
                    }
                }
            }
        }
        return "YES";

    }
    
}