## Between Two Sets

You will be given two arrays of integers. You will be asked to determine all integers that satisfy the following two conditions:

- The elements of the first array are all factors of the integer being considered
- The integer being considered is a factor of all elements of the second array

These numbers are referred to as being *between* the two arrays. You must determine how many such numbers exist.

**Input Format**

The first line contains two space-separated integers describing the respective values of , the number of elements in array , and , the number of elements in array .

The second line contains distinct space-separated integers describing .

The third line contains distinct space-separated integers describing .

**Constraints**

**Output Format**

Print the number of integers that are considered to be *between* and .

**Sample Input**

```
2 3
2 4
16 32 96
```

**Sample Output**

```
3
```

**Explanation**

2 and 4 divide evenly into 4, 8, 12 and 16.

4, 8 and 16 divide evenly into 16, 32, 96.

4, 8 and 16 are the only three numbers for which each element of A is a factor and each is a factor of all elements of B.