Demanding Guests

You are the manager of a newly opened luxury hotel in the Bahamas!
Each floor of the hotel consists of $N$ rooms (numbered  $1-N$ ) laid out in a straight line.

However, on your very first day of operations, you are faced with a particularly daunting challenge: accommodating a group of  $M$ guests (numbered $1-M$),  who have very specific demands.
You must quickly resolve this situation in order to avoid losing their patronage.
Their demands can be summarised as:

• Every guest has to be put up in a room on the same floor.
• This group wants to book all of the $N$ rooms on that floor!
• Any guest may be allocated more than one room.
• If a guest is assigned multiple rooms, these rooms should not be directly adjacent to each other.
  Example: If you decide to allocate $3$ rooms to guest number $1$, the distribution of rooms cannot be:
  . . . 1 1 . . .  or . . . 1 1 1 . . . 
• A particular guest, let us call him/her $X$ wants to be allocated at least the last room - the room numbered $N$.
• Guest number $1$ wants to be allocated atleast the 1st room - the room numbered $1$.

Thankfully, they do not have any specific demands regarding which room(s) are to be assigned to each of them, as such you are free to come up with a room allocation scheme that follows all of the above constraints.
Remember: Each guest, may be allocated any number of rooms including zero (except $X$ , $1$, must be allocated at least 1 room)

Your task is to determine how many such room allocation schemes are possible, since this number may be very large, print it modulo ${10}^9+7$.

Constraints:
$3<=N<={10}^5$
$2<=M<={10}^5$
$1<=X<=M$

Example:

Input:  N=4, M=3, X=2
Output: 3

Approach

Java

public class DemandingGuests {
    public static void main(String args[]) throws Exception {
        int N = 4;
        int M = 3;
        int X = 2;

        int MOD = 1000000007;

        long num = 1;
        boolean less = true;

        for (int n = 1; n < N - 1; n++) {
            num = ((num + MOD + (less ? -1 : 1)) * (M - 1)) % MOD;
            less = !less;
        }
        num = ((num + MOD + (less ? -1 : 1)) * (M - 1)) % MOD;
        if (X == 1)
            System.out.println(num);
        else
            System.out.println((num + MOD + (less ? 1 : -1)) % MOD);
    }

}