KöMaL 2008 B4094

Is it possible to leave one out of the numbers $1, 2, \ldots, 2008$ so that the remaining 2007 numbers can be listed in an order $a_1, a_2, \ldots, a_{2007}$, in which the differences ${|a_1-a_2|}, {|a_2-a_3|}, \ldots, {|a_{2006}-a_{2007}|}, {|a_{2007}-a_1|}$ are all different?