elementary number theory - Find a function $M$ such that $M(x)=1 forall xneq 0$ and $M(0)=0$

Find a function $F$ from $S*S$ to $\{0,1\}$ where $S$ is the set of first $12$ positive integers such that :

$$F(a,b) = \begin{cases}0 &, \text{for $b \ge a$}\\ 1 & \text{otherwise }. \end{cases}$$

My Attempt:

$$F(a,b)=\left\lfloor\frac{a+12}{b+12}\right\rfloor G(a,b)$$

Let $G(a,b)=M(a-b)$,
Now we have to find a function $M$ from $S \cup P\cup {0}$($P$ is the set of first twelve negaive integers) to $(1,0)$ such that $M(0)=0$ and $M(x) =1 \forall x>1$

Since the limit does not exist at $0$ ,therefore I can't use trig or exponential function s etc.

Any help in direction would be appreciated.

PS: keep it as simple as possible. I am willing to use $\mod,floor$ and $abs$ to construct $M$