Lucky Number

Watashi loves M mm very much. One day, M mm gives Watashi a chance to choose a number between low and high, and if the choosen number is lucky, M mm will marry him.

M mm has 2 sequences, the first one is BLN (Basic Lucky Numbers), and the second one is BUN (Basic Unlucky Numbers). She says that a number is lucky if it's divisible by at least one number from BLN and not divisible by at least one number from BUN.

Obviously, Watashi doesn't know the numbers in these 2 sequences, and he asks M mm that how many lucky number are there in [low, high]?

Please help M mm calculate it, meanwhile, tell Watashi what is the probability that M mm marries him.

Input

The first line of each test case contains the numbers N_BLN (1 <= N_BLN <= 15), N_BUN (1 <= N_BUN <= 500), low, high (1 <= low <= high <= 10¹⁸).

The second and third line contain N_BLN and N_BUN integers, respectively. Each integer in sequences BLN and BUN is from interval [1, 32767].

The last test case is followed by four zero.

The input will contain no more than 50 test cases.

Output

For each test case output one number, the number of lucky number between low and high.

Sample Input

2 1 70 81
2 3
5
0 0 0 0

Sample Output

5

Hint

The lucky numbers in the sample are 72, 74, 76, 78, 81.

ZOJ Monthly, August 2009