A sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let $$D^{}_{}$$ be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of $$\lfloor D^{}_{}\rfloor$$? (For real $$x^{}_{}$$, $$\lfloor x^{}_{}\rfloor$$ is the greatest integer less than or equal to $$x^{}_{}$$.)

(第七届AIME1989 第11题)