You have an array of positive integers a[1], a[2], ..., a[n] and a set of bad prime numbers b₁, b₂, ..., b_m. The prime numbers that do not occur in the set b are considered good. The beauty of array a is the sum , where function f(s) is determined as follows:

• f(1) = 0;
• Let's assume that p is the minimum prime divisor of s. If p is a good prime, then , otherwise .

You are allowed to perform an arbitrary (probably zero) number of operations to improve array a. The operation of improvement is the following sequence of actions:

• Choose some number r (1 ≤ r ≤ n) and calculate the value g = GCD(a[1], a[2], ..., a[r]).
• Apply the assignments: , , ..., .

What is the maximum beauty of the array you can get?

The first line contains two integers n and m (1 ≤ n, m ≤ 5000) showing how many numbers are in the array and how many bad prime numbers there are.

The second line contains n space-separated integers a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 10⁹) — array a. The third line contains m space-separated integers b₁, b₂, ..., b_m (2 ≤ b₁ < b₂ < ... < b_m ≤ 10⁹) — the set of bad prime numbers.

Print a single integer — the answer to the problem.