A13346. Adding Powers

Suppose you are performing the following algorithm. There is an array $v_1, v_2, \dots, v_n$ 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 $pos$ ( $1 \le pos \le n$ ) 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?

The first line contains one integer $T$ ( $1 \le T \le 1000$ ) — 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 $k$ ( $1 \le n \le 30$ , $2 \le k \le 100$ ) — the size of arrays $v$ and $a$ and value $k$ used in the algorithm.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i \le 10^{16}$ ) — the array you'd like to achieve.

For each test case print YES (case insensitive) if you can achieve the array $a$ after some step or NO (case insensitive) otherwise.

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 $v_2$ .