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.*;
import java.util.*;
import java.math.*;

 
 public class S	{
		static class Pair  implements Comparable<Pair> {
   int a;
   int b;
   public Pair(int x,int y){a=x;b=y;}
   public Pair(){}
   public int compareTo(Pair p1){
      return a+b-p1.a-p1.b;
   }
@Override
public int hashCode() {
	final int prime = 31;
	int result = 1;
	result = prime * result + a;
	result = prime * result + b;
	return result;
}
@Override
public boolean equals(Object obj) {
	Pair p = (Pair)obj;
	if (this.a==p.a && this.b==p.b)
		return true;
	else return false;
	
}
     
   
 }
static class TrieNode{
  TrieNode[]child;
  int w;
  boolean term;
  TrieNode(){
    child = new TrieNode[26];  
  }
}
  public static int gcd(int a,int b)
  {
    if(a<b)

      return gcd(b,a);
    if(b==0)
      return a;
    return gcd(b,a%b);
    
  }
  //static long ans = 0;
  static long mod = 998244353;//(long)(1e9+7);
   
    public static void main(String[] args) throws Exception {
       new Thread(null, null, "Anshum Gupta", 99999999) {
            public void run() {
                try {
                    solve();
                } catch(Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

static long pow(long x,long y){
    if(y == 0)return 1;
    if(y==1)return x;
    long a = pow(x,y/2);
    a = (a*a)%mod;
    if(y%2==0){
        return a;
    }
    return (a*x)%mod;
}

static long mxx;
static int mxN = (int)(1e5+5);

static long[]convert(long a,long k){
	ArrayList<Long> temp = new ArrayList<>();
	int i = 0;
	while(a > 0) {
		long rem = a % k;
		//temp.add(rem);
		if(rem!=0&&rem!=1)return new long[0];	
		temp.add(rem);
		a/=k;
		i++;
	}
	long[]ans=new long[temp.size()];
	for( i=0;i<temp.size();i++) {
		ans[i] = temp.get(i);
	}
	return ans;
}
 public static void solve() throws Exception {
   // solve the problem here
   MyScanner s = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out), true);
        int t = s.nextInt();
        mxx = (long)(1e18+5);
//        long []temp = convert(59049,9);
//        for(int c=0;c<temp.length;c++) {
//        	out.print(temp[c]);
//        }
        while(t-->0){
        	int n = s.nextInt();
        	int k = s.nextInt();
        	long[]a=new long[n];
        	long[][]base_k = new long[n][];
        	boolean ans = true;
        	HashSet<Integer> pows = new HashSet<Integer>();
        	for(int i=0;i<n;i++) {
        		a[i] = s.nextLong();
        		if(a[i]==0)continue;
        		base_k[i] = convert(a[i],k);
        		if(base_k[i].length==0) {
        			ans = false;
        		}
        		for(int j=base_k[i].length-1;j>=0;j--) {
        			if(base_k[i][j]==0)continue;
        			if(base_k[i][j]==1&&pows.contains(j)) {
        				ans = false;
        				break;
        			}
        			else pows.add(j);
        		}
        	}
        	
        	out.println(ans?"yes":"no");
        }
           
        out.flush();
}
 
     
 
 
 
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
 
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }
         
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}
