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.IOException;
import java.io.InputStream;
import java.util.*;
public class devesh08
{
public static void main(String args[])throws Exception 
{
FastReader in=new FastReader(System.in);
int t=in.nextInt(),i,j;
StringBuilder sb=new StringBuilder();
start:while(t-->0) 
{
	int n=in.nextInt();
	int k=in.nextInt(),z=0;
	long a[]=new long[60];
	for(i=0;i<n;i++)
	{
		long x=in.nextLong();
		j=0;
		while(x>0)
		{
			a[j]+=x%k;
			//System.out.print(a[j]);
			x=x/k;
			j++;
		}
		//System.out.println();
	}
	/*for(i=0;i<60;i++)
			System.out.println(dp[i]+" "+i);
		System.out.println();*/
	for(i=0;i<60;i++)
	{
		if(a[i]>1)
		{
			System.out.println("NO");
			continue start;
		}
	}
	System.out.println("YES");
}
}
}
class FastReader {
    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;
    FastReader(InputStream is) {
        in = is;
    }
    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }
    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    String nextLine() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c != 10 && c != 13; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }
    char nextChar() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        return (char) c;
    }
    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}


/*
	String s=in.nextInt();
			int n=s.length(),x=0;
			int vis[]=new int[26];
			ArrayList<Integer> ar=new AtrayList<>();
			if(n<4)
			{
				for(i=0;i<n;i++)
				{
					x=s.charAt(i)-'a';
					if(vis[x]==0)
						res+=s.charAt(i);
					vis[x]=1;
				}
				for(i=0;i<26;i++)
				{
					if(vis[i]==0)
						res+=(char)(i+97);
				}
				System.out.println("YES");
				System.out.println(res);
			}
			else
			{
			*/

			
			
			
			
			
