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.
//package Random;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Test {

    static int SixteenBits = 0xFFFF;//( '&' with this to get first 16 bits of a number)

    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;
        }
    }

    static int LowerBound(int a[], int x) { // x is the target value or key
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] >= x) r = m;
            else l = m;
        }
        return r;
    }

    static int UpperBound(int a[], int x) {// x is the key or target value
        int l = -1, r = a.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (a[m] <= x) l = m;
            else r = m;
        }
        return l + 1;
    }

    static int gcd(int a, int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    public static char compare(int i,int j,String s) {
        if (i + 1 == j && s.charAt(i) == s.charAt(j)) {
            return 'i';
        }

        if (i == j) {
            return 'i';


        }
        i++;
        j--;
        if (s.charAt(i) == s.charAt(j)) {
            compare(i, j, s);
        } else if (s.charAt(i) > s.charAt(j)) {
            return 'j';
        }
        return 'i';
    }

    static TreeSet<Long> s= new TreeSet<>();

    public static void main(String[] args) {
        FastReader sc = new FastReader();

        int t = sc.nextInt();

        while(t-->0){

            s = new TreeSet<>();

            int n = sc.nextInt();
            int k = sc.nextInt();

            Long[] arr = new Long[n];

            long max =0;

            for(int i=0;i<n;i++) {
                arr[i] = sc.nextLong();
                if(max<arr[i]){
                    max=arr[i];
                }
            }

            int i =0;
            while(true){

                long temp = (long) Math.pow(k,i);

                if(temp>max) {
                    s.add(temp);
                    break;
                }
                s.add(temp);
                i++;
            }

            Arrays.sort(arr);
            boolean flag =true;
            //System.out.println(s);
            for(i=0;i<n;i++){
                //System.out.println(s);
                if(!power(arr[i])){
                       flag=false;
                       System.out.println("NO");
                       break;
                }
            }

            if(flag){
                System.out.println("YES");
            }



        }
    }

    private static boolean power(long i) {

       // System.out.println(i);

        if(i==0){
            return true;
        }

        if(s.contains(i)){
            s.remove(i);
            return true;
        }
        else{
            long temp=0;
            try{
                temp=s.lower(i);

            }catch (Exception e){
                return false;
            }
            i-=temp;
            s.remove(temp);
            return power(i);
        }


       // return false;
    }


}
