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 

$1 \le n, m \le 10^{9}$

$1 \le k \le 10^{5}$

$k < m$