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≤n,m≤109
1≤k≤105
k<m
In the first move, you can subtract 1, in the second move you can subtract 3, in the third move you can subtract 4. So, you can make n equal to -1 after 3 moves.