Consider two sets of positive integers, A= {a0,a1…an-1} andA= {b0,b1…bn-1} . We say that a positive integer, , is *between* sets and if the following conditions are satisfied:

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

In other words, some is between and if that value of satisfies for every in and also satisfies for every in . For example, if and , then our possible values are , and .

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

**Input Format**

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

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**

There are three values *between* and :

- :
- All the elements in evenly divide .
- evenly divides all the elements in .

- :
- All the elements in evenly divide .
- evenly divides all the elements in .

- :
- All the elements in evenly divide .
- evenly divides all the elements in .

Thus, we print as our answer.

Solution in PHP

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<?php $handle = fopen ("php://stdin","r"); fscanf($handle,"%d %d",$n,$m); $a_temp = fgets($handle); $a = explode(" ",$a_temp); array_walk($a,'intval'); $b_temp = fgets($handle); $b = explode(" ",$b_temp); array_walk($b,'intval'); $lower_bound = $a[$n-1]; $upper_bound = $b[0]; $count_x = 0; for($i = 1; $i <= $upper_bound; $i++){ $sum_mod = 0; for($j = 0; $j < $n; $j++){ if ($i%$a[$j]!=0) { $sum_mod=1; } } for($k = 0; $k < $m; $k++){ if ($b[$k] % $i) { $sum_mod =1; } } if($sum_mod == 0){ $count_x++; } } echo $count_x; ?>