P5539 [XR-3] Unknown Mother-Goose

Xiao X is given a positive integer $n$ and a set of positive integers $S$. He wants to know how many positive integers $x$ satisfy all of the following conditions: - $3 \le x \le n$ - There exists $a \in S$ such that $x \equiv 0 \pmod a$ - There exists $b \in S$ such that $x-1 \equiv 0 \pmod b$ - There exists $c \in S$ such that $x-2 \equiv 0 \pmod c$ Please help Xiao X compute the answer.

The first line contains two positive integers $n, |S|$, representing the given $n$ and the size of the set $S$. The second line contains $|S|$ positive integers, representing the elements in the set $S$. **Constraints:** - $3 \le n \le 10^9$. - $3 \le |S| \le 20$. - All elements in $S$ are less than $n$. Elements are not guaranteed to be distinct.

Output one integer in a single line, representing the answer.

[Sample $1$ Explanation] Only when $x = 6$: - $x \equiv 0 \pmod 2$ - $x \equiv 1 \pmod 5$ - $x \equiv 2 \pmod 4$ do the conditions hold. Translated by ChatGPT 5