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.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public final class Main
{
	static long mod = (long) 1e9 + 7;

	public static void main(String[] args) throws IOException
	{
		Scanner in = getScan(args);
		int tt = in.nextInt();
		while (tt-- > 0)
		{
			int n = in.nextInt();
			int k = in.nextInt();
			long[] a = new long[n];

			for (int i = 0; i < n; i++)
			{
				a[i] = in.nextLong();
			}

			Set<Long> used = new HashSet<>();
			boolean res = true;
			int i = 0;

			while (i < n && res)
			{
				long curr = a[i];
				long pow = 0;
				while (curr > 0 && res)
				{
					long rest = curr % k;
					if (rest > 1)
					{
						res = false;
						break;
					}
					else if (rest == 1 && !used.add(pow))
					{
						res = false;
						break;
					}

					curr = (curr - rest) / k;
					pow++;
				}
				i++;
			}
			System.out.println(res ? "YES" : "NO");
		}
	}

	public static int log2nlz(int bits)
	{
		if (bits == 0) return 0; // or throw exception
		return 31 - Integer.numberOfLeadingZeros(bits);
	}

	static Scanner getScan(String[] args) throws IOException
	{
		if (args.length == 0)
		{
			return new Scanner(System.in);
		}
		else
		{
			return new Scanner(new File(args[0]));
		}
	}

	static BufferedReader getBuffer(String[] args) throws IOException
	{
		if (args.length == 0)
		{
			return new BufferedReader(new InputStreamReader(System.in));
		}
		else
		{
			return new BufferedReader(new FileReader(args[0]));
		}
	}

}