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.



/*
 -> Written by <-
   -----------
  |J_O_B_E_E_L|
  |___________|
  |    ___    |
  |   (^_^)   |
  |  /( | )\  |
  |____|_|____|
*/

import java.lang.reflect.Array;
import java.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
import java.util.Map.*;

public class Test {
	static PrintWriter pw = new PrintWriter(System.out);
	static int k;
	static HashSet<Long> set;
    static boolean getpowers(long x) {
    	if (x == 0)
			return true ;
    	
		long pow = 1;
		while (pow <= x) {
			pow *= k;
			
		}
		pow /= k;
		if(set.contains(pow)) return false;
		set.add(pow);
		return getpowers(x-pow);
    }
    public static void main(String[] args) throws IOException, InterruptedException {
        Scanner sc = new Scanner(System.in);
         int t=sc.nextInt();
         out: while(t-->0) {
        	 int x=sc.nextInt();  k=sc.nextInt();
        	 set=new HashSet<>();
        	 boolean f=true;
        	 for(int i=0;i<x;i++) {
        		 long y=sc.nextLong();
        		  f&=getpowers(y);
        	 }
//        	 for(int i=0;i<x-1;i++) {
//        		 for(int j=i+1;j<x;j++) {
//        		 boolean f=set[i].intersects(set[j]);
//        		 if(f) {
//        			 pw.println("NO");
//        			 continue out;
//        		 }
//        		 }
//        	 }
//        	 
//        	 pw.println("YES");
        	 pw.println(f ? "YES":"NO");
         
         }
        pw.flush();
        pw.close();
    }
 
    
    static  class pair implements Comparable <pair>{
        int x,y; int x1; long y1;
        public pair(int x,int y){this.x=x; this.y=y;}

        public int compareTo(pair o) {
           if(y==o.y) return  x-o.x;
            return  y-o.y;
        }
        public pair(int x1, long y1) {
        	this.x1=x1;
        	this.y1=y1;
        }
        public String toString(){
            return  x+" "+y;
        }
        
    }

    static class Scanner {

        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int curbuf;
        private int lenbuf;

        public Scanner(InputStream in) {
            this.in = in;
            this.curbuf = this.lenbuf = 0;
        }

        public boolean hasNextByte() {
            if (curbuf >= lenbuf) {
                curbuf = 0;
                try {
                    lenbuf = in.read(buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0)
                    return false;
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[curbuf++];
            else
                return -1;
        }

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private void skip() {
            while (hasNextByte() && isSpaceChar(buffer[curbuf]))
                curbuf++;
        }

        public boolean hasNext() {
            skip();
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (!isSpaceChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            if (!hasNext())
                throw new NoSuchElementException();
            int c = readByte();
            while (isSpaceChar(c))
                c = readByte();
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = readByte();
            } while (!isSpaceChar(c));
            return (minus) ? -res : res;
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            int c = readByte();
            while (isSpaceChar(c))
                c = readByte();
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = readByte();
            } while (!isSpaceChar(c));
            return (minus) ? -res : res;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

    }

}