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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {
	static int T;
	static int N,K;
	static long  MAX_VALUE = 10000000000000000L;
	static long arr[];
	static boolean check[];
	
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		
		T = Integer.parseInt(br.readLine());
		StringBuilder sb = new StringBuilder();
		
		for(int t=1;t<=T;t++) {
			st = new StringTokenizer(br.readLine());
			N = Integer.parseInt(st.nextToken());
			K = Integer.parseInt(st.nextToken());
			arr = new long[N];
			
			st = new StringTokenizer(br.readLine());
			for(int i=0;i<N;i++)
				arr[i] =Long.parseLong(st.nextToken());
			
			boolean YN = true;
			if(K!=1) {
				long v = 1;
				for(;v<=MAX_VALUE;v=v*K) {}
				
					while(v!=0L) {
					for(int i=0;i<N;i++) {
						if(arr[i]==0)continue;
						if(arr[i]>=v) {
							arr[i]-=v;
							break;
						}
					}
					v= v/K;
				}
				Arrays.sort(arr);
				if(arr[N-1]!=0) {
					YN = false;
				}
			}
			if(YN) {
				sb.append("YES\n");
			}else {
				sb.append("NO\n");
			}
			
		}
		System.out.print(sb.toString());
	}
}
