I don't have all day!

Algebra Level 3

$1 \# ( 2\# (3\# (4\# \cdots (98 \# 99 )))\cdots )$

Let $\#$ denote a binary operator such that $\color{#D61F06}{a}\# \color{#3D99F6}{b} =\color{#D61F06}{a}+\color{#3D99F6}{b}+\color{#D61F06}{a}\color{#3D99F6}{b}$ . Then what is the value of the expression above?

Notation: $n!$ denote the factorial of $n$ .