Magic Formula 

You are given a quadratic function, f (n) = a x 2 + b x + c. You are also given a divisor d and a limit L. How many of the function values f (0), f (1),..., f (L) are divisible by d?

Input 

Input consists of a number of test cases. Each test case consists of a single line containing the numbers a b c d L ( -1000$\le$a, b, c$\le$1000, 1 < d < 1000000, 0$\le$L < 1000).

Input is terminated by a line containing `0 0 0 0 0' which should not be processed.

Output 

Print the answer for each test case (the number of function values f (0), f (1),..., f (L) divisible by d) on a separate line.

Sample Input 

0 0 10 5 100
0 0 10 6 100
1 2 3 4 5
1 2 3 4 5
0 0 0 0 0

Sample Output 

101
0
0
4