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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws Exception {
        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            int d = 0;
            while (20000000000000000l >= Math.pow(k, d)) {
                d++;
            }
            int[] a = new int[d];
            for (int j = 0; j < n; j++) {
                long z = sc.nextLong();
                if (z != 0) {
                    for (int I = d; I > -1; ) {
                        //pw.println("*");
                        if (z < (long)Math.pow(k, I)) {
                            I--;
                        } else {
                            a[I]++;
                            z -= (long)Math.pow(k, I);
                        }
                    }
                }
            }
            boolean ans = true;
            for (int j = 0; j < d; j++) {
                if (a[j] > 1) {
                    ans = false;
                    break;
                }
            }
            pw.println(ans ? "YES" : "NO");


        }


        pw.close();
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }

    static class pair implements Comparable<pair> {
        int x;
        int y;

        public pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

        public String toString() {
            return x + " " + y;
        }

        public int compareTo(pair other) {
            if (this.x == other.x) {
                return this.y - other.y;
            } else {
                return this.x - other.x;
            }
        }
    }

    static class tuble implements Comparable<tuble> {
        int x;
        int y;
        int z;

        public tuble(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public String toString() {
            return x + " " + y + " " + z;
        }

        public int compareTo(tuble other) {
            if (this.x == other.x) {
                return this.y - other.y;
            } else {
                return this.x - other.x;
            }
        }
    }

    public static long GCD(long a, long b) {
        if (b == 0)
            return a;
        if (a == 0)
            return b;
        return (a > b) ? GCD(a % b, b) : GCD(a, b % a);
    }

    public static long LCM(long a, long b) {
        return a * b / GCD(a, b);
    }

    public static long nCk(int n, int k) { // O(K)
        if (k > n) {
            return 0;
        }
        long res = 1;
        for (int i = 1; i <= k; i++) {
            res = ((n - k + i) * res / i) % 1000000007;
        }
        return res;
    }

    public static long C(int a, int b, long[][] s) {
        int m = (int) 1e9 + 7;
        if (s[a][b] >= 0) {
            return s[a][b];
        } else if (a < b | a < 0 | b < 0) {
            s[a][b] = 0;
            return 0;
        } else if (a == b | b == 0) {
            s[a][b] = 1;
            return 1;
        } else {
            return s[a][b] = (C(a - 1, b, s) % m + C(a - 1, b - 1, s) % m) % m;
        }

    }

    public static boolean isprime(long a) {
        if (a == 0 || a == 1) {
            return false;
        }
        if (a == 2) {
            return true;
        }
        for (int i = 2; i < Math.sqrt(a) + 1; i++) {
            if (a % i == 0) {
                return false;
            }
        }
        return true;
    }

    static Scanner sc = new Scanner(System.in);
    static PrintWriter pw = new PrintWriter(System.out);
}