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;
?>
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