You are given a sequence of positive integers $A=(A_1,A_2,\dots,A_N)$ of length $N$ and a positive integer $M$. Find the number, modulo $998244353$, of non-empty and not necessarily contiguous subsequences of $A$ such that the least common multiple (LCM) of the elements in the subsequence is $M$. Two subsequences are distinguished if they are taken from different positions in the sequence, even if they coincide as sequences. Also, the LCM of a sequence with a single element is that element itself.

The input is given from Standard Input in the following format:

```
$N$ $M$
$A_1$ $A_2$ $\ldots$ $A_N$
```

Print the answer.

-   $1 \leq N \leq 2 \times 10^5$
-   $1 \leq M \leq 10^{16}$
-   $1 \leq A_i \leq 10^{16}$
-   All input values are integers.

5

The subsequences of A whose elements have an LCM of 6 are (2,3),(2,3,6),(2,6),(3,6),(6); there are five of them.

16

Note that even if some subsequences coincide as sequences, they are distinguished if they are taken from different positions.