Consider two sets of positive integers, A and B . We say that a positive integer, x , is *between* sets and if the following conditions are satisfied:

- All elements in A are factors of x.
- x is a factor of all elements in B.

Given A and B, find and print the number of integers (i.e., possible x‘s) that are *between* the two sets.

**Input Format**

The first line contains two space-separated integers describing the respective values of n (the number of elements in set A) and m (the number of elements in set B).

The second line contains n distinct space-separated integers .

The third line contains m distinct space-separated integers .

**Constraints**

**Output Format**

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

**Sample Input**

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

**Sample Output**

```
3
```

**Explanation**

The integers that are *between* A={2,4 } and B={16,32,96}are 4,8 , and 16 .

**Solution**

```
I have used two utility functions. One of which accepts an integer and an array and
checks if all the elements of array are factor of the element.
The second function also takes an integer and an array as inputs and checks if the
element is factorial of each element of the array.
I have run a loop from max of array A to min of array B and checked if the elements
is passing for both utility functions, if yes then I am increasing the count.
Count is the final variable here which is being printed in the end.
```