Magic Formula

You are given a quadratic function f(n) = 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 Specification

The input consists of a number of test cases. Each test case consists of a single line containing the numbers a, b, c, d, and L (–1000 ≤ a, b, c ≤ 1000, 1 < d < 1 000 000, 0 ≤ L < 1000).

The input is terminated by a line containing “0 0 0 0 0”, which should not be processed.

Output Specification

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

Sample Input

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

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Output for Sample Input

1. 101
2. 0
3. 0
4. 4

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