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.util.*;

public class Main {

//    static Node root;
//
//    public static Node insert(Node root, int data) {
//        if(root == null) {
//            root = new Node(data);
//            return root;
//        }
//        Queue<Node> q = new LinkedList<>();
//        q.add(root);
//        while (!q.isEmpty()) {
//            Node temp = q.poll();
//            if(temp.left != null) {
//                q.add(temp.left);
//            } else {
//                temp.left = new Node(data);
//                return root;
//            }
//            if(temp.right != null) {
//                q.add(temp.right);
//            } else {
//                temp.right  = new Node(data);
//                return root;
//            }
//        }
//        return root;
//    }
//
//    public static void inorder(Node root) {
//        if(root != null) {
//            inorder(root.left);
//            System.out.println(root.data);
//            inorder(root.right);
//        }
//
//    }
//
//    public static Node delete(Node root, int val) {
//        if(root == null) return null;
//        if(root.left == null && root.right == null) {
//            if(root.data == val) {
//                root = null;
//                return root;
//            } else {
//                return root;
//            }
//        }
//        Node keyNode = null;
//        Node bottom = null;
//        Node temp = null;
//        Queue<Node> q = new LinkedList<>();
//        q.add(root);
//        while (!q.isEmpty()) {
//            temp = q.poll();
//            if(temp.data == val) {
//                keyNode = temp;
//            }
//            if(temp.left != null) {
//                q.add(temp.left);
//            }
//            if(temp.right != null) {
//                q.add(temp.right);
//            }
//        }
//        bottom = temp;
//        if(keyNode == null) {
//            return root;
//        }
//        q.clear();
//        q.add(root);
//        while (!q.isEmpty()) {
//            temp = q.poll();
//            if(temp == keyNode) {
//                keyNode.data = bottom.data;
//            }
//            if(temp.left != null) {
//                if(temp.left == bottom) {
//                    temp.left = null;
//                } else q.add(temp.left);
//            }
//            if(temp.right != null) {
//                if(temp.right == bottom) {
//                    temp.right = null;
//                } else q.add(temp.right);
//            }
//        }
//        return root;
//    }

    private static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
//        root = null;
//        root = insert(root, 4);
//        insert(root, 5);
//        root = delete(root, 4);
//        inorder(root);
        int t = sc.nextInt();
        while (t-- != 0) {
            boolean flag = false;
            int n, k;
            n = sc.nextInt();
            k = sc.nextInt();
            long a[] = new long[n];
            for (int i = 0; i < n; ++i) {
                a[i] = sc.nextLong();
            }
            boolean vis[] = new boolean[64];
            for (int i = 0; i < n; ++i) {
                int j = 0;
                while(a[i] > 0) {
                    long rem = a[i] % k;
                    a[i] /= k;
                    if(rem > 1) {
                        System.out.println("NO");
                        flag = true;
                        break ;
                    }
                    if(rem == 1 && !vis[j]) {
                        vis[j] = true;
                    }
                    else if(rem == 1 && vis[j]) {
                        System.out.println("NO");
                        flag = true;
                        break ;
                    }

                    j++;
                }
                if(flag) {
                    break;
                }
            }
            if(!flag) {
                System.out.println("YES");
            }
        }
    }

}