VMO 1997 Problem 2

n > 1 is any integer not divisible by 1997. Put $a_m$ = m + mn/1997 for m = 1, 2, ... , 1996 and $b_m$ = m + 1997m/n for m = 1, 2, ... , n-1. Arrange all the terms $a_i$, $b_j$ in a single sequence in ascending order. Show that the difference between any two consecutive terms is less than 2.