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.Arrays;
import java.util.Scanner;

public class DIV2C_Adding_Powers {

    private static final Scanner IN = new Scanner(new BufferedInputStream(System.in));
    private static final PrintWriter OUT = new PrintWriter(new OutputStreamWriter(System.out));

    int n, k;

    private void input() {
    }

    private void process() {
        int t = nextInt();

        while (t-- > 0) {
            n = nextInt();
            k = nextInt();
            long[] a = new long[n];

            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }

            if (Arrays.stream(a).filter(e -> e > 0).count() == 0) {
                OUT.println("YES");
                continue;
            }

            if (k == 1) {
                OUT.println("YES");
            } else {
                long pow = 1;

                while (pow <= 10000000000000000L) {
                    boolean ok = true;
                    int cnt = 0;

                    for (int i = 0; i < n; i++) {
                        if (a[i] % pow != 0) {
                            ok = false;
                            break;
                        } else {
                            if ((a[i] / pow) % k != 0) {
                                cnt++;
                            }
                        }
                    }

                    if (!ok || cnt > 1) {
                        OUT.println("NO");
                        break;
                    }

                    if (cnt == 1) {
                        boolean find = false;

                        for (int i = 0; i < a.length; i++) {
                            if ((a[i] / pow) % k == 1) {
                                find = true;
                                a[i] -= pow;
                                break;
                            }
                        }

                        if (!find) {
                            OUT.println("NO");
                            break;
                        }
                    }

                    if (Arrays.stream(a).filter(e -> e > 0).count() == 0) {
                        OUT.println("YES");
                        break;
                    }

                    pow *= k;
                }
            }
        }
    }

    private void output() {
        OUT.flush();
    }

    private static long nextLong() {
        try {
            if (IN.hasNext()) {
                return IN.nextLong();
            } else {
                throw new EOFException();
            }
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    private static int nextInt() {
        try {
            if (IN.hasNext()) {
                return IN.nextInt();
            } else {
                throw new EOFException();
            }
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    private static String nextStr() {
        try {
            if (IN.hasNext()) {
                return IN.next();
            } else {
                throw new EOFException();
            }
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public static void main(String[] args) throws IOException {
        DIV2C_Adding_Powers main = new DIV2C_Adding_Powers();
        main.input();
        main.process();
        main.output();
    }
}
