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;
const long double pi = acos(-1);
const long long int mod = 1e9 + 7;
bool sortbysec(pair<long long int, long long int> a,
               pair<long long int, long long int> b) {
  return (a.second < b.second);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  long long int t, n, i, j, k, len, x, y, z, c, f, flag, p, q, mx, mn, l, r,
      sum, ans, tmp, it, pos, avg, m, cnt;
  string s;
  char ch;
  vector<long long int> v;
  vector<pair<long long int, long long int>> vec;
  unordered_map<long long int, long long int> mappu;
  pair<long long int, long long int> pr;
  t = 1;
  cin >> t;
  while (t--) {
    f = 0;
    sum = 0;
    flag = 0;
    ans = 0;
    cnt = 0;
    v.clear();
    mappu.clear();
    vec.clear();
    cin >> n >> k;
    long long int a[n];
    priority_queue<long long int, vector<long long int>> pq;
    for (i = 0; i < n; i++) {
      cin >> tmp;
      a[i] = tmp;
      if (tmp) pq.push(tmp);
    }
    x = 1;
    while (x * k <= 1e17) x *= k;
    while (pq.size() && x >= 1) {
      tmp = pq.top();
      pq.pop();
      if (tmp >= x) {
        tmp -= x;
      }
      if (tmp) pq.push(tmp);
      x /= k;
    }
    priority_queue<long long int, vector<long long int>> pp = pq;
    if (pq.size() == 0)
      cout << "YES"
           << "\n";
    else
      cout << "NO"
           << "\n";
  }
  return 0;
}
