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.Scanner;

public class AddingPowersEduRound83C {

	public static void main(String[] args) {
		Scanner s =new Scanner(System.in);
		int t = s.nextInt();
		StringBuilder str= new StringBuilder();
		while(t-- > 0) {
			int n = s.nextInt();
			int k = s.nextInt();
			long arr[] =new long[n];
			
			for(int i = 0;i<n;i++) {
				arr[i] = s.nextLong();
			}
			
			long max = 1l;
			while(max <= (long)1e16) {
				max*=k;
			}
			boolean flag = true;
			while(max > 0) {
				int cur = 0;
				for(int i = 0;i<n;i++) {
					if(arr[i] == 0) continue;
					
					if(arr[i] >= max) {
						arr[i]-=max;
						cur++;
					}
					
				} 
				
				if(cur > 1) {
					flag = false;
					break;
				}
				max /= k;
			}
			for(long p : arr) {
				if(p != 0) {
					flag = false;
					break;
				}
			}
			if(flag)
				str.append("YES").append("\n");
			else str.append("NO").append("\n");
		}
		System.out.println(str);

	}

}
