citadel OA

### Problem Statement

You are given a number of people `n` and a number of groups `k`. Your task is to find the distinct options to form `k` contiguous groups out of the `n` people while respecting the following conditions:

1. In each option, the total of group si

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es the number of groups to form

**Returns:**

- `int`: a long integer that denotes the number of ways that `n` participants can be divided into `k` groups satisfying the conditions mentioned above.