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)