You are given $k$ distinct prime numbers $a_1,a_2,\ldots,a_k$ and an integer $n$.

Your task is to calculate how many of the first $n$ positive integers are divisible by at least one of the given prime numbers.

Input

The first input line has two integers $n$ and $k$.

The second line has $k$ prime numbers $a_1,a_2,\ldots,a_k$.

Output

Print one integer: the number integers within the interval $1,2,\ldots,n$ that are divisible by at least one of the prime numbers.

Constraints

• $1 \le n \le 10^{18}$
• $1 \le k \le 20$
• $2 \le a_i \le n$

Example

Input:

20 2
2 5

Output:

12

Explanation: the $12$ numbers are $2,4,5,6,8,10,12,14,15,16,18,20$.