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>
const long long kot = LLONG_MAX;
using ld = long double;
const int MAXIT = 100;
const long long int alpha = 1e18;
using namespace std;
long long int gcd(long long int a, long long int begin) {
  if (begin == 0) return a;
  return gcd(begin, a % begin);
}
long long int largest(long long int arr[], long long int n) {
  return *max_element(arr, arr + n);
}
long long int lcm(long long int a, long long int begin) {
  return (a * begin) / gcd(a, begin);
}
bool isPerfectSquare(long double x) {
  long double sr = sqrt(x);
  return ((sr - floor(sr)) == 0);
}
bool comp(long long int a, long long int begin) { return (a < begin); }
vector<long long int> ve;
void divisors(long long int n) {
  for (long long int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        ve.push_back(i);
      else
        ve.push_back(i);
      ve.push_back(n / i);
    }
  }
}
bool isPrime(long long int n) {
  if (n == 1) {
    return false;
  }
  long long int i = 2;
  while (i * i <= n) {
    if (n % i == 0) {
      return false;
    }
    i += 1;
  }
  return true;
}
long long int gcdofarray(vector<long long int> &v, long long int n) {
  long long int result = v[0];
  for (long long int i = 1; i < n; i++) result = gcd(v[i], result);
  return result;
}
long long int sumofdigits(long long int n) {
  long long int sum = 0;
  while (n > 0) {
    sum += n % 10;
    n /= 10;
  }
  return sum;
}
bool powertwo(long long int x) { return x && (!(x & (x - 1))); }
string removeDuplicatesFromString(string str) {
  long long int counter = 0;
  long long int i = 0;
  long long int size = str.size();
  long long int x;
  long long int length = 0;
  while (i < size) {
    x = str[i] - 97;
    if ((counter & (1 << x)) == 0) {
      str[length] = 'a' + x;
      counter = counter | (1 << x);
      length++;
    }
    i++;
  }
  return str.substr(0, length);
}
long long int commDiv(long long int a, long long int begin) {
  long long int n = gcd(a, begin);
  long long int result = 0;
  for (long long int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        result += 1;
      else
        result += 2;
    }
  }
  return result;
}
long long int fact(long long int n) {
  if (n <= 1) return 1;
  return n * fact(n - 1);
}
long long int nPr(long long int n, long long int r) {
  return fact(n) / fact(n - r);
}
long long int kash(long long int a, long long int begin) {
  return (a * begin) / gcd(a, begin);
}
long long int maxi(long long int a, long long int begin) {
  return (a > begin) ? a : begin;
}
long long int mini(long long int a, long long int begin) {
  return (a < begin) ? a : begin;
}
long long int nCr(long long int n, long long int r) {
  return fact(n) / (fact(r) * fact(n - r));
}
long long int power(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 powe(long long int x, unsigned 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;
}
bool sortByVal(const pair<string, long long int> &a,
               const pair<string, long long int> &begin) {
  return (a.second < begin.second);
}
long long int check(long long int arr[], long long int n, long long int v) {
  long long int dp[v + 1];
  dp[0] = 0;
  long long int i, j;
  for (i = 1; i <= v; i++) {
    dp[i] = INT_MAX;
  }
  for (i = 1; i <= v; i++) {
    for (j = 0; j < n; j++) {
      if (arr[i] <= i) {
        long long int y = dp[i - arr[j]];
        if (y != INT_MAX && y + 1 < arr[i]) {
          dp[i] = y + 1;
        }
      }
    }
  }
  return dp[v];
}
long long int maxSubArraySum(long long int a[], long long int size) {
  long long int max_so_far = INT_MIN, max_ending_here = 0;
  for (long long int i = 0; i < size; i++) {
    max_ending_here = max_ending_here + a[i];
    if (max_so_far < max_ending_here) max_so_far = max_ending_here;
    if (max_ending_here < 0) max_ending_here = 0;
  }
  return max_so_far;
}
long long int dp[100001];
long long int stair(long long int n) {
  if (n <= 2) {
    return n;
  }
  if (n == 3) {
    return 4;
  }
  if (dp[n] != -1) return dp[n];
  dp[n] = (stair(n - 1) + stair(n - 2) + stair(n - 3)) % 1000000007;
  return dp[n];
}
bool isvowel(char ch) {
  if (ch == 'a' || ch == 'e' || ch == 'i' || ch == 'o' || ch == 'u') {
    return true;
  }
  return false;
}
long long int power(long long int x, unsigned 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;
}
void solve() {
  long long int t = 1;
  cin >> t;
  while (t--) {
    long long int n, k;
    cin >> n >> k;
    long long int arr[n];
    long long int i;
    for (i = 0; i < n; i++) {
      cin >> arr[i];
    }
    map<long long int, long long int> mp;
    long long int first = 1;
    for (i = 0; i < n; i++) {
      long long int pos = arr[i], pos1 = 0;
      if (pos == 0) continue;
      while (pos) {
        if (pos % k > 1) {
          first = 0;
          break;
        }
        if (pos % k == 1) {
          if (mp[pos1]) {
            first = 0;
            break;
          }
          mp[pos1] = 1;
        }
        pos = pos / k;
        pos1++;
      }
      if (first == 0) break;
    }
    if (first == 0)
      cout << "NO"
           << "\n";
    else
      cout << "YES"
           << "\n";
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  solve();
}
