P10704 Redemption

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

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 $998244353$.

The first line contains two integers $n$ and $m$. The second line contains $n$ integers $a_1, a_2 \dots a_n$.

Output one integer, the result modulo $998244353$.

#### 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 | | :----------: | :----------: | :----------: | :----------: | :----------: | :----------: | | $0$ | $\le 10^2$ | $\le 10^{6}$ | $\le 10^5$ | $10$ | $-$ | | $1$ | $\le 10^4$ | $\le 10^{10}$ | $\le 10^9$ | $10$ | $-$ | | $2$ | $\le 10^6$ | $\le 10^{10}$ | $\le 10^4$ | $10$ | $-$ | | $3$ | $\le 10^6$ | $\le 10^8$ | $\le 10^9$ | $20$ | $-$ | | $4$ | $\le 10^6$ | $\le 10^{10}$ | $\le 10^9$ | $20$ | $A$ | | $5$ | $\le 10^6$ | $\le 10^{10}$ | $\le 10^9$ | $30$ | $-$ | 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