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.
//   package com.company;
  import java.util.*;
  import java.io.*;
  import java.lang.*;
  /*
  ** @author jigar_nainuji
   */
  public class Main{

      public static void main(String args[]){
          PrintWriter out=new PrintWriter(System.out);
          InputReader in=new InputReader(System.in);
          TASK solver = new TASK();
          int t = in.nextInt();
//          int t=1;
            for(int i=0;i<t;i++)
            {
                solver.solve(in,out,i);
            }
            out.close();
      }
      static class TASK{
          static boolean CheckForSequence(ArrayList<Long> dp,TreeSet<Long> set,
                                           long k)
          {
              // Traverse the array from end
              // to start
//              ArrayList<Long> al = new ArrayList<>();
              for (int i =dp.size()-1; i >= 0; i--)
              {
                  if (k >= dp.get(i) && set.contains(dp.get(i))) {
                      k -= dp.get(i);
                      set.remove(dp.get(i));
                  }
              }

              // If there is any subsequence
              // whose sum is equal to k
              if (k != 0)
                  return false;
              else
                  return true;
          }
          void solve(InputReader in,PrintWriter out,int testNumber) {

                  int n = in.nextInt();
                  int k = in.nextInt();
                  long max = 0;
                  long a[] = new long[n];
                  for(int i=0;i<n;i++)
                  {
                      a[i]=in.nextLong();
                      max=Math.max(a[i],max);

                  }
                  TreeSet<Long> set = new TreeSet<>();
                  ArrayList<Long> dp = new ArrayList<>();
                  dp.add(1l);
                  set.add(1l);
                  for(int i=1;i<63;i++)
                  {
                      dp.add(k*dp.get(i-1));
                      set.add(dp.get(i));
                      if(dp.get(i)>=max)
                          break;
                  }
                  Arrays.sort(a);
                  int count=0;
                  for(int j=0;j<n;j++)
                  {
//                      System.out.println(set);
                      count++;
                      if(a[j]==0)
                          continue;
                      if(!CheckForSequence(dp,set,a[j]))
                      {
                          System.out.println("NO");
                          return;
                      }
                  }
              System.out.println("YES");
          }
      }
      static class Maths{
          static long gcd(long a, long b) {
              if (a == 0)
                  return b;
              return gcd(b % a, a);
          }

          public  static long lcm(long a, long b)
          {
              return (a*b)/gcd(a, b);
          }

          public static long factorial(int n){
              long fact = 1;
              for(int i=1;i<=n;i++){
                  fact *= i;
              }
              return fact;
          }
      }
      static class InputReader {
          private InputStream stream;
          private byte[] buf = new byte[1024];
          private int curChar;
          private int numChars;
          private SpaceCharFilter filter;

          public InputReader(InputStream stream) {
              this.stream = stream;
          }

          public int read() {
              if (numChars == -1)
                  throw new InputMismatchException();

              if (curChar >= numChars) {
                  curChar = 0;
                  try {
                      numChars = stream.read(buf);
                  } catch (IOException e) {
                      throw new InputMismatchException();
                  }

                  if (numChars <= 0)
                      return -1;
              }
              return buf[curChar++];
          }

          public String nextLine() {
              BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
              String str = "";
              try {
                  str = br.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return str;
          }

          public int nextInt() {
              int c = read();

              while (isSpaceChar(c))
                  c = read();

              int sgn = 1;

              if (c == '-') {
                  sgn = -1;
                  c = read();
              }

              int res = 0;
              do {
                  if (c < '0' || c > '9')
                      throw new InputMismatchException();
                  res *= 10;
                  res += c - '0';
                  c = read();
              }
              while (!isSpaceChar(c));

              return res * sgn;
          }

          public long nextLong() {
              int c = read();
              while (isSpaceChar(c))
                  c = read();
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
              long res = 0;

              do {
                  if (c < '0' || c > '9')
                      throw new InputMismatchException();
                  res *= 10;
                  res += c - '0';
                  c = read();
              }
              while (!isSpaceChar(c));
              return res * sgn;
          }

          public double nextDouble() {
              int c = read();
              while (isSpaceChar(c))
                  c = read();
              int sgn = 1;
              if (c == '-') {
                  sgn = -1;
                  c = read();
              }
              double res = 0;
              while (!isSpaceChar(c) && c != '.') {
                  if (c == 'e' || c == 'E')
                      return res * Math.pow(10, nextInt());
                  if (c < '0' || c > '9')
                      throw new InputMismatchException();
                  res *= 10;
                  res += c - '0';
                  c = read();
              }
              if (c == '.') {
                  c = read();
                  double m = 1;
                  while (!isSpaceChar(c)) {
                      if (c == 'e' || c == 'E')
                          return res * Math.pow(10, nextInt());
                      if (c < '0' || c > '9')
                          throw new InputMismatchException();
                      m /= 10;
                      res += (c - '0') * m;
                      c = read();
                  }
              }
              return res * sgn;
          }

          public String readString() {
              int c = read();
              while (isSpaceChar(c))
                  c = read();
              StringBuilder res = new StringBuilder();
              do {
                  res.appendCodePoint(c);
                  c = read();
              }
              while (!isSpaceChar(c));

              return res.toString();
          }

          public boolean isSpaceChar(int c) {
              if (filter != null)
                  return filter.isSpaceChar(c);
              return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
          }

          public String next() {
              return readString();
          }

          public interface SpaceCharFilter {
              public boolean isSpaceChar(int ch);
          }
      }
  }