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.
#include <bits/stdc++.h>
using namespace std;
long long int mod = 1000000007;
vector<long long int> initializeDiffArray(vector<long long int>& A);
void update(vector<long long int>& D, long long int l, long long int r,
            long long int x);
void getArray(vector<long long int>& A, vector<long long int>& D);
long long int min(long long int a, long long int b);
long long int max(long long int a, long long int b);
long long int gcd(long long int a, long long int b);
void swap(long long int* a, long long int* b);
long long int lcm(long long int a, long long int b);
long long int modpower(long long int x, long long int y, long long int p);
long long int power(long long int x, long long int y);
long long int modulo(long long int value, long long int m);
long long int myXOR(long long int x, long long int y);
long long int diff(long long int a, long long int b);
int main() {
  {
    ios ::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
  };
  long long int rep = 1;
  cin >> rep;
  while (rep--) {
    long long int n, k;
    cin >> n >> k;
    long long int a[n];
    for (long long int i = 0; i <= n - 1; ++i) cin >> a[i];
    long long int flag = 1;
    string s[n];
    for (long long int i = 0; i <= n - 1; ++i) {
      s[i] = "";
      for (long long int j = 0; j <= 60; ++j) {
        if (a[i] % k == 0)
          s[i] += '0';
        else if (a[i] % k != 1) {
          flag = 0;
          s[i] += '1';
        } else {
          s[i] += '1';
        }
        a[i] /= k;
      }
    }
    if (flag) {
      for (long long int i = 0; i <= 60; ++i) {
        long long int c = 0;
        for (long long int j = 0; j <= n - 1; ++j) {
          if (s[j][i] == '1') c++;
        }
        if (c > 1) flag = 0;
      }
      if (flag)
        cout << "YES" << '\n';
      else
        cout << "NO" << '\n';
    } else
      cout << "NO" << '\n';
  }
  return 0;
}
long long int myXOR(long long int x, long long int y) {
  return (x | y) & (~x | ~y);
}
long long int min(long long int a, long long int b) {
  if (a > b) return b;
  return a;
}
long long int max(long long int a, long long int b) {
  if (a < b) return b;
  return a;
}
long long int gcd(long long int a, long long int b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long int diff(long long int a, long long int b) {
  if (a > b) return a - b;
  return b - a;
}
void swap(long long int* a, long long int* b) {
  long long int t = *a;
  *a = *b;
  *b = t;
}
long long int lcm(long long int a, long long int b) {
  if (a == 0) return b;
  if (b == 0) return a;
  return (a * b) / gcd(a, b);
}
long long int modpower(long long int x, long long int y, long long int p) {
  long long int res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long int power(long long int x, long long int y) {
  long long int temp;
  if (y == 0) return 1;
  temp = power(x, y / 2);
  if (y % 2 == 0)
    return temp * temp;
  else
    return x * temp * temp;
}
long long int modulo(long long int value, long long int m) {
  long long int mod = value % m;
  if (value < 0) {
    mod += m;
  }
  return mod;
}
vector<long long int> initializeDiffArray(vector<long long int>& A) {
  long long int n = A.size();
  vector<long long int> D(n + 1);
  D[0] = A[0], D[n] = 0;
  for (long long int i = 1; i < n; i++) D[i] = A[i] - A[i - 1];
  return D;
}
void update(vector<long long int>& D, long long int l, long long int r,
            long long int x) {
  D[l] += x;
  D[r + 1] -= x;
}
void getArray(vector<long long int>& A, vector<long long int>& D) {
  for (long long int i = 0; i < A.size(); i++) {
    if (i == 0)
      A[i] = D[i];
    else
      A[i] = D[i] + A[i - 1];
  }
}
