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.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Solution {
	
	public static void main(String[] args) {

		/*
		 * 8
13 -2 -11 5 6 2 -11 -2
		 */
		Solution sl=new Solution();
		Scanner scan = new Scanner(System.in);
		
		//System.out.println(getPows(100, 4)); if(true)return;
		 
		int t = scan.nextInt();
		while(t-->0) {
			int n =scan.nextInt();
			int k =scan.nextInt();
			long[] arr = new long[n];
			for(int i=0;i<n;i++) {
				arr[i]=scan.nextLong();
			}
			Set<Integer> pows = new HashSet<Integer>();
			boolean flag=true;
			outer:for(int i=0;i<n;i++) {
				if(arr[i]==0) continue;
				if(arr[i]==1) {
					if(pows.contains(0)) {
						flag=false;
						break;
					}
					pows.add(0);
				}else {
					Set<Integer> res=null;
					if(arr[i]%k==0 ) {
						res = getPows(arr[i],k);
					}else if((arr[i]-1)%k==0) {
						res = getPows(arr[i]-1,k);
						if(res.isEmpty()) {
							flag=false;
							break;
						}
						res.add(0);
					}else {
						flag=false;
						break;
					}
					//Set<Integer> res = getPows(arr[i],k);
					if(res.isEmpty()) {
						flag=false;
						break;
					}
					for(int num:res) {
						if(pows.contains(num)) {
							flag=false;
							break outer;
						}
						pows.add(num);
					}
				}
			}
			if(flag) System.out.println("YES");
			else System.out.println("NO");
		}
		
		
		scan.close();
	}
	
	public static Set<Integer> getPows(long n, int k){
		Set<Integer> ans = new HashSet<Integer>();
		if(n==0) {
			ans.add(0);
			return ans;
		}if(n==1 || n%k!=0) {
			return ans;
		}
		int pow=0;
		while(n%Math.pow(k, pow)==0) {
			pow++;
		}
		pow--;
		long rem=n/(long)Math.pow(k, pow);
		Set<Integer> res=getPows(rem-1,k);
		if(res.isEmpty()) return res;
		ans.add(pow);
		for(int num:res) {
			
			ans.add(pow+num);
		}
		return ans;
	}
	
	/*
	 * static final Random random=new Random();
	 * 
	 * static void ruffleSort(int[] a) { int n=a.length; //shuffle, then sort for
	 * for(int i=0; i<n; i++) { int oi=random.nextInt(n), temp=a[oi]; a[oi]=a[i];
	 * a[i]=temp; } Arrays.sort(a); }
	 */
	 
	
}