Apples and Worms 2

Problem Description

You bought a box of $n$ apples, but unfortunately a worm had gotten mixed into the box. The worm can eat one apple every $x$ hours, and it will not start on another apple until it has finished the current one. After $y$ hours, how many intact apples do you still have?

Input Format

One line containing $n, x$ and $y$ (all integers).

Output Format

One line containing the number of remaining apples.

Sample Input

10 4 9

Sample Output

7

Hint

• Same model as "Apples and Worms": round the number eaten up to the ceiling; do not let the answer go negative.
• Here $x$ is guaranteed to be at least $1$, so you need not worry about division by zero.
• Check against the sample: 10 4 9 → 7.