Background

There are $n$ robots in Workshop Alpha and $m$ robots in Workshop Beta. Every robot has a unique-looking serial number, and two robots become compatible when the serial number of the Alpha robot is a divisor of the serial number of the Beta robot.

The factory wants to know how many compatible cross-workshop pairs can be formed.

Problem

You are given two sequences:

• $A_1, A_2, \dots, A_n$: serial numbers of the robots in Workshop Alpha;
• $B_1, B_2, \dots, B_m$: serial numbers of the robots in Workshop Beta.

Count the number of pairs $(i, j)$ such that $1 \le i \le n$, $1 \le j \le m$, and

$$B_j \bmod A_i = 0.$$

Input Format

The first line contains two integers $n$ and $m$, separated by a space.

The second line contains $n$ integers $A_1, A_2, \dots, A_n$.

The third line contains $m$ integers $B_1, B_2, \dots, B_m$.

Output Format

Output a single integer: the number of compatible pairs.

Samples

Sample 1

Input:

2 3
2 3
2 6 9

Output:

4

Explanation:

$2$ divides $2$ and $6$; $3$ divides $6$ and $9$. There are $4$ compatible pairs.

Sample 2

Input:

3 3
2 2 5
4 10 5

Output:

6

Explanation:

Each of the two $2$'s matches $4$ and $10$; the single $5$ matches $10$ and $5$. The total is $2 \times 2 + 1 \times 2 = 6$.

Constraints

• $1 \le n, m \le 2 \times 10^5$
• $1 \le A_i, B_j \le 10^6$

The answer may exceed the range of a 32-bit signed integer.