Synchronized Dance Performance

A professional dance company is preparing a spectacular synchronized performance. The choreography calls for $N$ dancers to be arranged in a single line formation, with male and female dancers positioned according to the artistic vision. During the performance, certain dancers will execute impressive partner lifts that require coordination and strength.

The choreographer has designed the lifts with safety in mind: each lift must be performed by two male dancers standing adjacent to each other in the formation. One dancer acts as the primary lifter while the adjacent male dancer provides spotting support. Two female dancers cannot perform a lift together, nor can a male and female dancer standing next to each other (as the choreography requires both participants to have the strength for this specific technique).

The artistic director now faces an interesting challenge: how many different ways can the male and female dancers be arranged in the line to satisfy the following conditions?

1. There are exactly $N$ dancers in the formation.

2. Exactly $K$ lifts must be performed by the dancers.

3. If two male dancers stand next to each other, they must perform a lift together, with one partnering from the left side and the other from the right side.

4. If a male dancer is flanked by two other male dancers, he participates in lifts on both his left and right sides.

5. If a female dancer stands to the left (or right) of a male dancer, he does not participate in a lift on his left (or right) side.

6. If there is no one to the left (or right) of a male dancer, he does not participate in a lift on his left (or right) side.

For example, if there are $5$ dancers in the formation who must perform $2$ lifts, there are $6$ possible arrangements.