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.