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.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {

	public static void main(String[] args) throws NumberFormatException, IOException
	{
		new B().run();
	}
	
	public void run() throws NumberFormatException, IOException {
		BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		int T = Integer.parseInt(file.readLine());
	looperino:
		for(int i = 0;i<T;i++)
		{
			int[] num = new int[100];
			st = new StringTokenizer(file.readLine());
			int N = Integer.parseInt(st.nextToken());
			int K = Integer.parseInt(st.nextToken());
			long[] ints = new long[N];
			st = new StringTokenizer(file.readLine());
			for(int j = 0;j<N;j++)
			{
				long l = Long.parseLong(st.nextToken());
				convert(l,K, num);
			}
			//System.out.println(Arrays.toString(num));
			for(int x: num)
			{
				if(x > 1)
				{
					System.out.println("NO");
					continue looperino;
				}
			}
			System.out.println("YES");
		}
	}
	
	public void convert(long i, int base, int[] num)
	{
		int pos = 0;
		while(i != 0)
		{
			num[pos]+=i%base;
			i /= base;
			pos++;
		}
	}
	
}
