C. Adding Powerstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputSuppose 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?InputThe 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.OutputFor each test case print YES (case insensitive) if you can achieve the array a after some step or NO (case insensitive) otherwise.ExampleInput
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
NoteIn 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.
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 
['bitmasks', 'greedy', 'implementation', 'math', 'number theory', 'ternary search', '*1400']