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.*;

public class AddingPower {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner sc = new Scanner(System.in);

		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int k = sc.nextInt();
			long[] arr = new long[n];
			long max = (long) 1e16;
			long pow=1;
			for(int i=0;i<arr.length;i++) {
				arr[i]=sc.nextLong();
			}
			while(pow<max) {
				pow=pow*k;
			}
			
			boolean flag=false;
			while(pow!=0) {
				int count=0;
				for(int i=0;i<arr.length;i++) {
					if(arr[i]>=pow) {
						arr[i]=arr[i]-pow;
						count++;
					}
					
				}
				if(count>1) {
					flag=true;
					
				}
				if(flag) {
					break;
				}
				pow=pow/k;
			}
			
			if(flag) {
				System.out.println("NO");
			}else {
				int count=0;
				for(int i=0;i<arr.length;i++) {
					if(arr[i]!=0) {
						count++;
					}
				}
				if(count>0) {
					System.out.println("NO");
				}else {
					System.out.println("YES");
				}
			}
			
			
			
		}
	}

}
