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.Comparator;
import java.util.StringTokenizer;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author User
 */
public class Edu_83_Div2_C {

    static 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;
        }
    }

    static class Var {

        int a, b;

        Var(int x, int y) {
            a = x;
            b = y;
        }
    }

    static class Comp implements Comparator<Var> {

        public int compare(Var o1, Var o2) {
            if (o1.b < o2.b) {
                return 1;
            } else {
                return -1;
            }
        }
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            long a[] = new long[n];
            long k = sc.nextInt();
            long max = 0;
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextLong();
                if (a[i] > max) {
                    max = a[i];
                }
            }
            int c = 0;
            while (max > 0) {
                ++c;
                max = max / k;
            }
            long arr[][] = new long[n][c];
            int flag = 0;
            
            for (int i = 0; i < n; i++) {
                long x = a[i];
                int idx = c - 1;
                while (x > 0) {
                    long r = x % k;
                    if (r > 1) {
                        flag = 1;
                        break;
                    } else {
                        arr[i][idx--] = r;
                        x = x / k;
                    }
                }
                if (flag == 1) {
                    break;
                }
            }
            if (flag == 1) {
                System.out.println("NO");
                continue;
            }
            for (int i = 0; i < c; i++) {
                int s = 0;
                for (int j = 0; j < n; j++) {
                    s += arr[j][i];
                }
                if (s > 1) {
                    flag = 1;
                    break;
                }                
            }
            if (flag == 1) {
                System.out.println("NO");
                continue;
            }
            System.out.println("YES");

        }
    }
}
