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

public class Main{
    public static void main(String[] args) {
        InputReader sc = new InputReader(System.in);
//                Scanner sc = new Scanner(System.in);

        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            int n = sc.nextInt();
            Long x = sc.nextLong();
            Long[] aa = new Long[n];
            for (int j = 0; j < n; j++) {
                aa[j] = sc.nextLong();//数组
            }
            if (solution(x, aa)) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }

        }

    }

    static boolean solution(Long x, Long[] aa) {
//        insertSort(aa);//从小到大

        HashMap<Integer, Integer> map = new HashMap<>();
        ArrayList<Integer> list = new ArrayList<>();
        HashSet<Integer> set = new HashSet<>();
        int count = 0;

        if(x == 1){
            return true;
        }

        for(int i =0 ;i < aa.length; i++){
            map = solve(x,aa[i]);
            if(map.isEmpty()){
                return false;
            }else {
                for(int j = 0; j< map.size(); j++){
                    if(map.get(j) != -1){
                        count++;
//                        list.add(map.get(j));
                        set.add(map.get(j));
                    }
                }
            }
        }
        if(count > set.size()){
            return false;
        }

        return true;

    }

    static HashMap<Integer,Integer> solve(Long x, Long a){
        Long yu = 0L;
        int count  = 0;
        int k = 0;
        HashMap<Integer, Integer> map = new HashMap();
        if(x == 1){return new HashMap<>();}
        if(a < x){
            if(a > 1){
                return new HashMap();
            }
            if(a == 1){
                map.put(k++,count);
            }
            if(a == 0){
                map.put(k++, -1);
            }
        }else {
            while (a >= x){
                yu = a % x;
                if(yu != 1 && yu != 0){
                    return new HashMap();

                }else {
                    if(yu == 1){
                        map.put(k++,count);
                    }
                }
                a  = a / x;
                count++;
            }
            if(a != 1){
                return new HashMap();
            }else {
                map.put(k++,count);
            }
        }


        return map;
    }


    static class InputReader {
        public BufferedReader br = null;
        StringTokenizer tokenizer = null;

        public InputReader(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(br.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());
        }
    }
}
/*

5
3 7
0 0 0
1 10
1
3 6
1 6 1
3 3
0 1 4
3 3
0 243 36



* */

  	 	 		    					 			 	 	 	 			