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 Main{
	private static Scanner cin = new Scanner(new BufferedInputStream(System.in));
	private static PrintWriter cout = new PrintWriter(System.out,true);
	private static InputStream inputstream = System.in;
	private static FastScanner in = new FastScanner(inputstream);
	public static void main(String[] args){
		Task solver = new Task();
		int TaskCase = in.nextInt();
		while(TaskCase--!=0) solver.solve();
		cout.flush();
	}
	private static class Task{
		private long overflow = (long)1e16;
		public void solve(){
			int n = in.nextInt(), k = in.nextInt();
			Long A[] = new Long[n];
			for(int i = 0; i < n; i++) A[i] = in.nextLong();
			int cur = 64;
			while(cur!=-1){
				long p = pow((long)k,cur);
				if(p==-1){
					cur--;
					continue;
				}
				int pos = 0;
				for(int i = 1; i < n; i++) if(A[i]>A[pos]) pos = i;
				if(A[pos]>=p) A[pos] -= p;
				cur--;
			}
			boolean ok = true;
			for(int i = 0; i < n; i++) if(A[i]!=0){
				ok = false;
				//cout.print(A[i]); cout.print(' ');
				break;
			}
			if(ok) cout.println("YES");
			else cout.println("NO");
		}
		private long pow(long a, long b){
			long res = 1;
			while(b!=0){
				res = res * a;
				if(res>overflow) return -1l;
				b-=1;
			}
			return res;
		}
	}
	public static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(InputStream in) {
				br = new BufferedReader(new InputStreamReader(in));
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public boolean hasMoreTokens() {
			while (st == null || !st.hasMoreElements()) {
				String line = null;
				try {
					line = br.readLine();
				} catch (IOException e) {
					return false;
				}
				if (line == null) {
					return false;
				}
				st = new StringTokenizer(line);
			}
			return true;
		}
		public String next() {
			while (st == null || !st.hasMoreElements()) {
				String line = null;
				try {
					line = br.readLine();
				} catch (IOException e) {
				}
				st = new StringTokenizer(line);
			}
			return st.nextToken();
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public int[] nextIntArray(int n) {
			int[] ret = new int[n];
			for (int i = 0; i < n; i++) {
				ret[i] = nextInt();
			}
			return ret;
		}
		public long[] nextLongArray(int n) {
			long[] ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] = nextLong();
			}
			return ret;
		}
	}
}