#P1312C. Adding Powers
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ID: 5236
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Adding Powers
No submission language available for this problem.
Description
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.
Input
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.
Output
For each test case print YES (case insensitive) if you can achieve the array $a$ after some step or NO (case insensitive) otherwise.
Samples
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
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 $v_2$.