Problem Description

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

Calculate:

\[ \sum_{i=1}^{n} \sum_{j=1}^{n} \left\lfloor \frac{m}{a_i a_j} \right\rfloor \]

Output the result modulo \( 998244353 \).

Input Format

The first line contains two integers \( n \) and \( m \).

The second line contains \( n \) integers \( a_1, a_2, \ldots, a_n \).

Output Format

Output a single integer representing the result modulo \( 998244353 \).

Sample Input and Output

Sample Input #1

5 30
2 2 8 4 2

Sample Output #1

88

Sample Input #2

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

Sample Output #2

2715

Notes

Sample Explanation

The contributions in the first sample are as follows:

• \((a_1, a_1): \left\lfloor \frac{30}{2 \times 2} \right\rfloor = 7\)
• \((a_1, a_2), (a_2, a_1): \left\lfloor \frac{30}{2 \times 2} \right\rfloor \times 2 = 14\)
• \((a_1, a_3), (a_3, a_1): \left\lfloor \frac{30}{2 \times 8} \right\rfloor \times 2 = 2\)
• \((a_1, a_4), (a_4, a_1): \left\lfloor \frac{30}{2 \times 4} \right\rfloor \times 2 = 6\)
• \((a_1, a_5), (a_5, a_1): \left\lfloor \frac{30}{2 \times 2} \right\rfloor \times 2 = 14\)
• \((a_2, a_2): \left\lfloor \frac{30}{2 \times 2} \right\rfloor = 7\)
• \((a_2, a_3), (a_3, a_2): \left\lfloor \frac{30}{2 \times 8} \right\rfloor \times 2 = 2\)
• \((a_2, a_4), (a_4, a_2): \left\lfloor \frac{30}{2 \times 4} \right\rfloor \times 2 = 6\)
• \((a_2, a_5), (a_5, a_2): \left\lfloor \frac{30}{2 \times 2} \right\rfloor \times 2 = 14\)
• \((a_3, a_5), (a_5, a_3): \left\lfloor \frac{30}{2 \times 8} \right\rfloor \times 2 = 2\)
• \((a_4, a_4): \left\lfloor \frac{30}{4 \times 4} \right\rfloor = 1\)
• \((a_4, a_5), (a_5, a_4): \left\lfloor \frac{30}{2 \times 4} \right\rfloor \times 2 = 6\)
• \((a_5, a_5): \left\lfloor \frac{30}{2 \times 2} \right\rfloor = 7\)

Summing these contributions: \( 7 + 14 + 2 + 6 + 14 + 7 + 2 + 6 + 14 + 2 + 1 + 6 + 7 = 88 \).

Data Range

Special Property A: \(\sum_{i=1}^{n} a_i \le 10^7\).

For \( 100\% \) of the data, \( 1 \le n \le 10^6 \), \( 1 \le a_i \le 10^9 \), \(\sum_{i=1}^{n} a_i \le 10^9 \), \( 1 \le m \le 10^{10} \).

Special Note: This problem uses subtask-based scoring. You must pass all test cases in a subtask to earn the points for that subtask.

见题面 Input 部分

见题面 Output 部分