Integer Game

Jaehyun plays an integer game with the following rules.

1. Fix an integer $N$ and an array $A$ of length $K$.
2. Write every integer from $1$ to $N$ on a sheet of paper.
3. Take the first number of $A$ and remove it from the array. Calling that number $x$, erase every multiple of $x$ written on the paper.
4. Repeat step 3 until the array is empty.

Write a program that counts how many numbers are still written on the paper after the game ends.

The first line contains $N$ and $K$. ($1 \le N \le 10^9$, $1 \le K \le 15$)

The second line contains the $K$ elements of $A$ in order. Each element is a natural number at most $100$, and the same number may appear more than once.

Print on the first line how many numbers are still written on the paper after the game ends.

If $N$ is $10$ and the array is $[2, 4, 5]$, you erase the multiples of $2$, then of $4$, then of $5$, and the paper keeps $1$, $3$, $7$ and $9$.