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;
template <typename T>
void print(const T& v) {
  cerr << v << ' ';
}
template <typename T1, typename... T2>
void print(const T1& first, const T2&... rest) {
  print(first);
  print(rest...);
}
typedef priority_queue<pair<int, int>, vector<pair<int, int> >,
                       greater<pair<int, int> > >
    pq;
int setbit(int N, int pos) { return N = N | (1 << pos); }
int resetbit(int N, int pos) { return N = N & ~(1 << pos); }
bool checkbit(int N, int pos) { return (bool)(N & (1 << pos)); }
int nextN(int N) { return N + (N & (-N)); }
int parentN(int N) { return N - (N & (-N)); }
template <typename T>
T extGcd(T a, T b, T& x, T& y) {
  if (a == 0) {
    x = 0, y = 1;
    return b;
  }
  T x1, y1, gcd = extGcd(b % a, a, &x1, &y1);
  x = y1 - (b / a) * x1, y = x1;
  return gcd;
}
template <typename T>
T bigMod(T a, T p, T m) {
  if (p == 1) return a;
  T x = bigMod(a, p / 2, m) % m;
  x = (x * x) % m;
  return (p & 1) ? (x * a) % m : x;
}
template <typename T>
T modMul(T a, T b, T m) {
  return ((a % m) * (b % m)) % m;
}
template <typename T>
T modAdd(T a, T b, T m) {
  return ((a % m) + (b % m)) % m;
}
template <typename T>
T modSub(T a, T b, T m) {
  return (a - b + m) % m;
}
template <typename T>
T modInverse(T a, T m) {
  return bigMod(a, m - 2, m);
}
bool pw[100];
bool solve(long long x, int k) {
  if (x == 0) return true;
  long long mx = 0, p = 1;
  int i = -1;
  while (p <= x) {
    mx = p;
    i++;
    p *= k;
  }
  long long cur = mx;
  while (cur > 0 && x > 0) {
    if (cur <= x) {
      if (!pw[i]) return false;
      x -= cur;
      pw[i] = 0;
    }
    cur /= k;
    i--;
  }
  if (x > 0) return false;
  return true;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int t, n, k;
  long long a[33];
  cin >> t;
  while (t--) {
    cin >> n >> k;
    memset(pw, true, sizeof pw);
    bool f = 1;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    for (int i = 1; i <= n; ++i) {
      if (!solve(a[i], k)) {
        f = 0;
        break;
      };
    }
    if (f)
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
  return 0;
}
