#11934Magic Formula

You are given a quadratic function, f (x) = ax2 + bx + 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 ≤ a, b, c ≤ 1000, 1 < d < 1000000, 0 ≤ 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.

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

101
0
0
4