Practice on Toph
Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.
Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.
You’ll be given an array of $N$
integers and two more integers $K$
and $M$
. You have to find the number of lcm divisible subsequence of length $M$
in that array.
A subsequence of length $M$
is called lcm divisible subsequence if the LCM (Lowest Common Multiple) of all the numbers in that subsequence is divisible by $K$
. For example, if $A = [2, 2, 3, 4, 7, 6]$
, $M = 3$
and $K = 6$
, then $(2, 2, 6)$
is a valid lcm divisible subsequence. Because the length of this subsequence is $M = 3$
and the LCM is $6$
, which is divisible by $K = 6$
.
Note: A subsequence in the array $A$
is a sequence that can be derived by deleting some or no elements without changing the order of the remaining elements in the array $A$
. Two subsequences are considered different if the chosen indices are different.
$1 \leq T \leq 5 $
$1 \leq N \leq 100000 $
$1 \leq M \leq 1000 $
$1 \leq K, A_i \leq 50000 $
The first line of the input contains a single integer $T$
denoting the number of test cases, then $T$
test cases follow. The first line of a test case contains three integers $N$
, $M$
and $K$
. The following line of the test case contains $N$
space separated integers of the array $A$
.
For each test case print a single integer, the number of lcm divisible subsequence in the given array. Since the answer can be quite large, you have to compute it modulo $998244353$
.
Input  Output 

5 3 2 2 2 3 4 4 3 9 2 4 5 6 5 3 6 2 8 12 5 6 6 3 6 2 2 3 4 7 6 10 3 6 2 3 6 12 16 18 20 25 9 24  3 0 9 16 115 
In the first test case, the list of valid lcm divisible subsequence is given below:
In the second test case, there’s no valid lcm divisible subsequence. In the third test case, some valid lcm divisible subsequences are given below:
