Several distinct real numbers are written on a blackboard. Peter wants to make an expression such that its values are exactly these numbers. To make such an expression, he may use any real numbers, brackets, and usual signs $+$ , $-$ and $\times$. He may also use a special sign $\pm$: computing the values of the resulting expression, he chooses values $+$ or $-$ for every $\pm$ in all possible combinations. For instance, the expression $5 \pm 1$ results in $\{4, 6 \}$, and $(2 \pm 0.5) \pm 0.5$ results in $\{1, 2, 3 \}$. Can Pete construct such an expression: $a)$ If the numbers on the blackboard are $1, 2, 4$; $b)$ For any collection of $100$ distinct real numbers on a blackboard?