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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Ap1312C {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scanner = new Scanner(System.in);
		int t = scanner.nextInt();
		for (int i = 0; i < t; i++) {
			int n = scanner.nextInt();
			long k = scanner.nextLong();
			boolean terminate = false;
			Set<Integer> indices = new HashSet<Integer>();
			int indexSize = 0;
			long[] a = new long[n];
			for(int j=0;j<n;j++) {
				a[j] = scanner.nextLong();
			}
			for (int j = 0; j < n; j++) {
				if(terminate)
					break;
				int count = 0;
				long quotient = a[j];
				while (quotient != 0) {
					long newQuotient = quotient / k;
					long newRemainder = quotient % k;
					if (newRemainder == 1) {
						quotient = quotient - 1;
						// System.out.println(quotient);
						indices.add(count);
						if (indices.size() == indexSize) {
							System.out.println("NO");
							terminate = true;
							break;
						}
						else {
							indexSize = indices.size();
						}
					} else if(newRemainder ==  0){
						quotient = newQuotient;
						count++;
					} else {
						System.out.println("NO");
						terminate = true;
						break;
					}
				}
			}
			if (!terminate) {
				System.out.println("YES");
				// System.out.println(indices);
		}
		}
		scanner.close();
	}

}
