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.*;
public class MyClass {
    
    public static void main(String args[]) {
      FastReader sc = new FastReader();     //For Fast IO
      //func f = new func();                  //Call func for swap , permute, upper bound and for sort.
      int t = sc.nextInt();
      while(t-->0){
          int n = sc.nextInt();
          int k = sc.nextInt();
          int f=0;
          long arr[] = new long[n];
          for(int i=0;i<n;i++){
              arr[i]=sc.nextLong();
          }
          HashMap<Integer,Integer> hs = new HashMap<>();
          for(int i=0;i<n;i++){
              ArrayList<Long> al = new ArrayList<>();
              while(arr[i]>0){
                  al.add(arr[i]%k);
                  arr[i] = arr[i]/k;
              }
              for(int j=0;j<al.size();j++){
                  if(al.get(j)!= 0 && al.get(j)!=1){
                      f=1;
                      break;
                  }
              }
              if(f==1){break;}
              for(int j=0;j<al.size();j++){
                  if(al.get(j)==1){
                      if(hs.get(j)==null){
                          hs.put(j,1);
                      }
                      else{
                          f=1;
                          break;
                      }
                  }
              }
              if(f==1){break;}
          }
          
          
          if(f==0){
              System.out.println("YES");
          }
          else{
              System.out.println("NO");
          }
      }
      
      
      
    }
}
class Pair{
    int x;
    int y;
    Pair(int i,int j){
        x=i;
        y=j;
    }
    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (!(o instanceof Pair)) return false;
        Pair key = (Pair) o;
        return x == key.x && y == key.y;
    }
    @Override
    public int hashCode() {
        int result = x;
        result = 31*result + y;
        return result;
    }
}
class FastReader 
	{ 
		BufferedReader br; 
		StringTokenizer st; 
 
		public FastReader() 
		{ 
			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; 
		} 
	}
class func{
    static ArrayList<String> al = new ArrayList<>();
        public static void sort(long[] arr) {
            int n = arr.length, mid, h, s, l, i, j, k;
            long[] res = new long[n];
            for (s = 1; s < n; s <<= 1) {
                for (l = 0; l < n - 1; l += (s << 1)) {
                    h = Math.min(l + (s << 1) - 1, n - 1);
                    mid = Math.min(l + s - 1, n - 1);
                    i = l;
                    j = mid + 1;
                    k = l;
                    while (i <= mid && j <= h) res[k++] = (arr[i] <= arr[j] ? arr[i++] : arr[j++]);
                    while (i <= mid) res[k++] = arr[i++];
                    while (j <= h) res[k++] = arr[j++];
                    for (k = l; k <= h; k++) arr[k] = res[k];
                }
            }
        }
        public static void permute(char a[] , int i , int n){
            if(i==n-1){
                String s = new String(a);
                al.add(s);                      // al stores all permutations of string. 
                return;
            }
            for(int j=i;j<n;j++){
                swap(a,i,j);
                permute(a,i+1,n);
                swap(a,i,j);
            }
        }
        public static void swap(char a[],int i, int j){
            char temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }
        public static void swap(int a[],int i, int j){
            int temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }
		//-It returns index of first element which is strictly greater than searched value.
		public static int upperBound(long[] array, int length, long value) {
            int low = 0;
            int high = length;
            while (low < high) {
                final int mid = (low + high) / 2;
                if (value >= array[mid]) {
                    low = mid + 1;
                } else {
                    high = mid;
                }
        }
        return low;
    }
	/*If searched element doesn't exist function returns index of first element which is bigger than searched value.<br>
 * -If searched element is bigger than any array element function returns first index after last element.<br>
 * -If searched element is lower than any array element function returns index of first element.<br>
 * -If there are many values equals searched value function returns first occurrence.<br>*/
	public static int lowerBound(long[] array, int length, long value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value <= array[mid]) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }
        
 
}



	 	 
