In how many different ways can I arrange $n$ girls and $m$ boys with no at least $k$ boys or $k$ girls sit next to each other?

Question

For example, we have $n = 5$ boys and $m = 6$ girls, we don't want $k \le min(n, m)$ | $k = 3$ boys or girls to sit next to each other.

A valid arrangement: $BBGGBGGBGG$

An invalid arrangement: $BBBGGBGGBGG$ - There are $3$ boys sit next to each other.

And we ignore the permutation between any group of boys and girls so $BBGGBGGBGG$ is considered only $1$ way