Virologist Abutalib continues his mathematical calculations. He is searching for effective ways to detect positive or negative tests for coronavirus. Abutalib has coronavirus tests numbered from to . In the course of his calculations, he found that positive tests satisfy certain conditions. Specifically, a test is considered positive if its serial number is divisible by numbers previously determined by Abutalib, and at the same time, is not divisible by other numbers also determined by Abutalib. You should help Abutalib to determine how many tests from to are positive.
The first line contains integers and (1 \leq a \leq b \leq 10^{18}).
The second line contains integers and (0 \leq k, m \leq 20).
The third line contains integers x_i (1 \leq x_i \leq 10^{18}) — numbers that must divide the positive test.
The fourth line contains integers y_i (1 \leq y_i \leq 10^{18}) — numbers that must not divide the positive test.
Print the number of positive tests from to .
Example 1
Example 2
Example 3