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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.StringTokenizer;


public class COVID {

	

public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int t= sc.nextInt();
		
		all:while(t-->0) {
		
			int n=sc.nextInt();int k=sc.nextInt();
			
			long[] arr=new long[n];
			
			for(int i=0;i<n;i++) {
				arr[i]=sc.nextLong();
				
			}
			HashSet<Integer> set =new HashSet<Integer>();
			
			for(int i=0;i<n;i++)
			{
				while(arr[i]>0) {
					int log =log(arr[i], k);
				//	System.out.println(log);
					long pow=pow(k, log);
					arr[i]-=pow;
					//System.out.println(arr[i]+" "+ pow);
					int nlog=log(arr[i],k);
					if(set.contains(log)||(log==nlog&&arr[i]!=0)) {
						pw.println("NO");
						continue all;
					}
					set.add(log);
					
				}
			}
			pw.println("YES");
		}
		pw.flush();
	}
static int Log2n(long n) 
{ 
    return (n > 1) ? 1 + Log2n(n / 2) : 0; 
} 
static int log(long n, long r) 
{ 
    return (n > r - 1) ? 1 + log(n / r, r) : 0; 
} 
 
//public static int log(long x,int base) {
//	if(x==0)return 0;
// return(int) Math.floor(Math.log(x)/Math.log(base)+(1e-5));
//}
static int log(long x) {
	int ans=0;
	
	while(x>1) {
		x/=2;
ans++;		
	}
	return ans;
	}
public static long pow(long x ,int p) {// loop O(log p )
	long ans=1;
	while(p>0) {
		
		if((p&1)==1) 
			ans= (ans*x);
	x=(x*x);
	p>>=1;
	}
	return ans;
}
static class pair{
	int x,y;
	public pair(int a, int b) {
		this.x=a;y=b;
	}
	@Override
	public int hashCode() {
		final int prime = 31;
		int result = 1;
		result = prime * result + x;
		result = prime * result + y;
		return result;
	}
	@Override
	public boolean equals(Object obj) {
		if (this == obj)
			return true;
		if (obj == null)
			return false;
		if (getClass() != obj.getClass())
			return false;
		pair other = (pair) obj;
		if (x != other.x)
			return false;
		if (y != other.y)
			return false;
		return true;
	}
	
}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++) {
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
				if (sb.length() == 18) {
					res += Long.parseLong(sb.toString()) / f;
					sb = new StringBuilder("0");
				}
			}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

	public static void shuffle(int[] a) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}
}
