You are given three integers \(n\), \(m\), and \(k\). In a single move, you can subtract any integer in the range from \(1\) to \(m\) from \(n\), but you are not be allowed to subtract this integer during the next \(k\) moves. What is the minimum number of moves required to make \(n\) strictly smaller than 0?
 

Input format

The first and only line of input contains three integers \(-\) \(n, m, k\)

Output format

Print an integer denoting the answer to the problem.

Constraints 

\(1 \le n, m \le 10^{9}\)

\(1 \le k \le 10^{5}\)

\(k < m\)