Climbing Stairs with Variable Step Sizes

You are given a staircase with n steps. You can climb the staircase by taking steps of any size from 1 up to m. Your task is to compute the number of distinct ways to reach exactly the n^th step. The recurrence relation that governs the process is given by:

$$dp[i] = \sum_{j=1}^{\min(m,i)} dp[i-j]$$

where dp[i] represents the number of ways to reach step i with the base case dp[0] = 1. This problem tests your understanding of dynamic programming and counting techniques.

inputFormat

The input is provided via standard input (stdin) as two space-separated integers:

• n (1 ≤ n ≤ 10⁴): the total number of steps in the staircase.
• m (1 ≤ m ≤ n): the maximum step size you are allowed to take.

outputFormat

Output a single integer to standard output (stdout) representing the total number of distinct ways to climb the staircase.

5 2

8