If $S=\{ax+by: x,y\in \mathbb{Z^+} \}$ then $ab-a-b$ is the maximum element in $\mathbb{N} \setminus S$. [duplicate]

Let $$a,b$$ be positive relatively prime integers and $$S$$ be a set defined by $$\{ax+by: x,y\in \mathbb{Z^+} \}$$. I want to show that $$ab-a-b$$ is the maximum element in $$\mathbb{N} \setminus S$$.

We need to show that $$ab-a-b+k \in S$$ for all positive integers $$k$$ and $$ab-a-b$$ is not in $$S$$. Do you have any idea? Thanks.