Minimum Maximum Distance Between Water Stations

You are given a race track of length \(L\) and allowed to place exactly \(N\) water stations along the track, including the endpoints.

Your goal is to arrange the water stations such that the maximum distance between any two consecutive stations is minimized. Although an extra parameter \(D\) is provided (representing a maximum allowed distance between consecutive stations), it is not used in the optimal arrangement calculation.

For example, if \(L = 10\), \(N = 3\), and \(D = 4\), the optimal arrangement yields a maximum gap of \(4\).

Input: Three integers \(L\), \(N\), and \(D\) in one line separated by spaces.

Output: A single integer representing the minimum possible value of the maximum distance between consecutive water stations.

inputFormat

A single line with three integers: L N D (separated by spaces).

outputFormat

A single integer: the minimized maximum distance between consecutive water stations.## sample

10 3 4

4