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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class AddingPowers {
    public static void main(String[] args) {

        // (9^2) * (9+1) => 9^3 + 9^^
        Scanner scanner = new Scanner(System.in);
        int test = scanner.nextInt();
        scanner.nextLine();

        for (int t = 0; t < test; t++) {
            int n = scanner.nextInt();
            long k = scanner.nextLong();
            scanner.nextLine();

            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = scanner.nextLong();
            }
            scanner.nextLine();

            boolean isValid = true;
            List<Integer> nums = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (arr[i] != 0) {
                    List<Integer> decomposedList = decompose(arr[i], k);
                    if (decomposedList.isEmpty()) {
                        isValid = false;
                        break;
                    }
                    nums.addAll(decomposedList);
                }
            }

            if (!isValid) {
                System.out.println("NO");
            }else{
                Collections.sort(nums);
                boolean valid = true;

                for (int i = 0; i < nums.size(); i++) {
                    if (i != 0) {
                        if (nums.get(i) == nums.get(i - 1)) {
                            valid = false;
                            break;
                        }
                    }
                }

                System.out.println(valid ? "YES" : "NO");

            }

        }

        // 91 * 9^2
        // (1 + 90) * 9^2
        // (1 + 9 * 10) * 9^2
        // 9^2 + 9^3 * (9 + 1)
        // 9^^ + 9^4 + 9^^



    }

    // 81 + 27 = 27 ( 1 + 3)
    // 243 + 81 + 27 = 27 * (1 + 3 + 9)
    private static List<Integer> decompose(long i, long k) {
        List<Integer> result = new ArrayList<>();
        int count = 0;
        boolean isValid = true;
        while (i != 1) {
            if (i % k == 0) {
                i /= k;
                count++;
            }else{
                i -= 1;
                result.add(count);
                if (i % k != 0) {
                    isValid = false;
                    break;
                }

            }
        }
        if (!isValid) {
            return new ArrayList<>();
        }

        if (i == 1) {
            result.add(count);
        }

        return result;

    }
}
