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;

public class Solution {
    private static boolean calc(long[] a, int k) {
        int deg = (int) (Math.log(10000000000000000L) / Math.log(k));
        long maxVal = (long) (Math.pow(k, deg));
        for (long part = maxVal; part > 0; part /= k) {
            boolean was = false;
            for (int i = 0; i < a.length; i++) {
                if (a[i] >= part){
                    if (was) return false;
                    was = true;
                    a[i] -= part;
                }
            }
        }
        for (long el : a) {
            if (el != 0) return false;
        }
        return true;
    }

//    public static void main(String[] args) {
//        System.out.println(calc(new long[]{281475010331664L, 1161226012856512L, 211106249326858L, 4525933457317920L, 2263897394382852L}, 2));
//    }

    public static void main(String[] args) throws IOException {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        int test = Integer.parseInt(bf.readLine());
        for (int t = 0; t < test; t++) {
            String[] nkStr = bf.readLine().split("\\s");
            int k = Integer.parseInt(nkStr[1]);
            String[] aStr = bf.readLine().split("\\s");
            long[] a = Arrays.stream(aStr).mapToLong(Long::parseLong).toArray();
            boolean can = calc(a, k);
            System.out.println(can ? "YES" : "NO");
        }
    }
}
