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;
bool change_base(int64_t x, int64_t k, vector<int64_t>& res) {
  if (x == 0) {
    res.push_back(0);
    return true;
  }
  while (x != 0) {
    if (x % k > 1) {
      return false;
    }
    res.push_back(x % k);
    x /= k;
  }
  return true;
}
bool good(int64_t x, int64_t k, int64_t n, vector<bool>& v) {
  vector<int64_t> res;
  res.reserve(n);
  auto okay = change_base(x, k, res);
  if (!okay) {
    return false;
  } else {
    int64_t len = res.size();
    for (int64_t i = 0; i < len; i++) {
      if (i >= v.size()) {
        v.push_back(true);
      }
      if (res[i] == 1) {
        if (!v[i]) {
          return false;
        } else {
          v[i] = false;
        }
      }
    }
    return true;
  }
}
int main() {
  ios::sync_with_stdio(false);
  int64_t tc;
  cin >> tc;
  for (int64_t tt = 0; tt < tc; tt++) {
    int64_t n;
    int64_t k;
    cin >> n >> k;
    vector<bool> v(n, true);
    vector<int64_t> res(n);
    bool okay = true;
    for (int64_t i = 0; i < n; i++) {
      cin >> res[i];
      if (okay && good(res[i], k, n, v)) {
        continue;
      } else {
        okay = false;
      }
    }
    if (!okay) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl;
    }
  }
  return 0;
}
