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>
#pragma GCC optimize("Ofast,no-stack-protector")
#pragma GCC optimize("unroll-loops")
using namespace std;
using ll = long long;
using ld = long double;
using VectorType = ld;
using ull = unsigned long long;
const ll INF = 1e15;
const ld eps = 1e-7;
const ld pi = atan2(0, -1);
const ll mod = 998244353;
const ll P = 179, Q = 239;
const ll A = 2;
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());
ll sign(ll a) {
  if (a < 0) return -1;
  if (a == 0) return 0;
  return 1;
}
bool equal(ld a, ld b) { return abs(a - b) < eps; }
struct query {
  ll l, r, i;
  query(ll l = 0, ll r = 0, ll i = 0) : l(l), r(r), i(i){};
};
bool mini(ll &a, ll b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
bool maxi(ll &a, ll b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}
bool mini(ld &a, ld b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
ll mmax(ll a, ll b) {
  if (a > b) return a;
  return b;
}
ll mmin(ll a, ll b) {
  if (a < b) return a;
  return b;
}
bool maxi(ld &a, ld b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}
ll sub(ll a, ll b) {
  a -= b;
  if (a < 0) {
    a += mod;
  }
  return a;
}
ll add(ll a, ll b) {
  a += b;
  if (a > mod) {
    a -= mod;
  }
  return a;
}
ll mul(ll a, ll b) { return (a * b) % mod; }
ll n, m;
ll k;
vector<vector<ll>> vec;
vector<bool> used;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  ll t;
  cin >> t;
  for (int i = 0; i < t; ++i) {
    cin >> n >> k;
    vector<ll> a(n);
    for (auto &x : a) {
      cin >> x;
    }
    map<ll, ll> cnt;
    for (auto &x : a) {
      vector<ll> cur;
      while (x >= k) {
        cur.push_back(x % k);
        x /= k;
      }
      cur.push_back(x);
      for (int i = 0; i < cur.size(); ++i) {
        cnt[i] += cur[i];
      }
    }
    bool ok = true;
    for (auto &x : cnt) {
      if (x.second > 1) {
        ok = false;
        break;
      }
    }
    if (ok) {
      cout << "YES\n";
    } else {
      cout << "NO\n";
    }
  }
  return 0;
}
