Problem Description

Find the sum of all natural numbers not exceeding $m$ whose set of prime factors intersects the given set of primes.

Input Format

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

The second line contains $n$ integers $p_i$, representing the elements of the prime set.

Output Format

Output one integer, the answer modulo $376544743$.

2 15
3 5

60

Hint

Sample explanation: All qualifying numbers are $3, 5, 6, 9, 10, 12, 15$, and their sum is $60$.

For the first $30\%$ of the testdata, $1 \le n, m$.

For the remaining $70\%$ of the testdata, $1 \le n \le 20$，$1 \le m \le {10}^9$.

Translated by ChatGPT 5