Background

$$Lord,$$ $$is this person also someone we must save\dots$$ $$May my barrage of bullets put out your suffering\dots$$$$If you see an angel who gives off an ominous aura,$$$$please tell her for me:$$ $$I have never forgotten her\dots$$

Problem Description

Given $n$, $m$, and $n$ integers $a_i$ ($1 \le i \le n$).

Compute:

$$\sum\limits_{i=1}^{n} \sum\limits_{j=1}^{n}\left \lfloor \frac{m}{a_i a_j} \right \rfloor$$

Output the result modulo $998244353$.

Input Format

The first line contains two integers $n$ and $m$.

The second line contains $n$ integers $a_1, a_2 \dots a_n$.

Output Format

Output one integer, the result modulo $998244353$.

5 30
2 2 8 4 2 

88

10 5035239199
4853 53137 86933 4465 13588 11899 49877 16317 43326 52183 

2715

Hint

Sample Explanation

The contributions in Sample 1 are as follows:

$(a_1, a_1): \left \lfloor \frac{30}{2\times 2} \right \rfloor = 7$.

$(a_1, a_2), (a_2, a_1): \left \lfloor \frac{30}{2\times 2} \right \rfloor \times 2 = 14$.

$(a_1, a_3), (a_3, a_1): \left \lfloor \frac{30}{2\times 8} \right \rfloor \times 2 = 2$.

$(a_1, a_4), (a_4, a_1): \left \lfloor \frac{30}{2\times 4} \right \rfloor \times 2 = 6$.

$(a_1, a_5), (a_5, a_1): \left \lfloor \frac{30}{2\times 2} \right \rfloor \times 2 = 14$.

$(a_2, a_2): \left \lfloor \frac{30}{2\times 2} \right \rfloor = 7$.

$(a_2, a_3), (a_3, a_2): \left \lfloor \frac{30}{2\times 8} \right \rfloor \times 2 = 2$.

$(a_2, a_4), (a_4, a_2): \left \lfloor \frac{30}{2\times 4} \right \rfloor \times 2 = 6$.

$(a_2, a_5), (a_5, a_2): \left \lfloor \frac{30}{2\times 2} \right \rfloor \times 2 = 14$.

$(a_3, a_5), (a_5, a_3): \left \lfloor \frac{30}{2\times 8} \right \rfloor \times 2 = 2$.

$(a_4, a_4): \left \lfloor \frac{30}{4\times 4} \right \rfloor = 1$.

$(a_4, a_5), (a_5, a_4): \left \lfloor \frac{30}{2\times 4} \right \rfloor \times 2 = 6$.

$(a_5, a_5): \left \lfloor \frac{30}{2\times 2} \right \rfloor = 7$.

$7 + 14 + 2 + 6 + 14 + 7 + 2 + 6 + 14 + 2 + 1 + 6 + 7 = 88$.

Constraints

Subtask ID	$n$	$m$	$a_i$	Score	Special Property
$0$	$\le 10^2$	$\le 10^{6}$	$\le 10^5$	$10$	$-$
$1$	$\le 10^4$	$\le 10^{10}$	$\le 10^9$
$2$	$\le 10^6$		$\le 10^4$
$3$		$\le 10^8$	$\le 10^9$	$20$
$4$		$\le 10^{10}$			$A$
$5$				$30$	$-$

Special property $A$: $\sum\limits_{i=1}^{n} a_i \le 10^7$.

For $100\%$ of the testdata: $1 \le n \le 10^6$, $1 \le a_i \le 10^9$, $\sum\limits_{i=1}^{n} a_i \le 10^9$, and $1 \le m \le 10^{10}$.

Special note: This problem uses bundled subtask testing. You can only get the score for a subtask after passing all test points in that subtask.

Translated by ChatGPT 5