IMO 1986 LL TUR72

Origin: TUR

Problem

A one-person game with two possible outcomes is played as follows: After each play, the player receives either a or b points, where a and b are integers with 0 < b < a < 1986. The game is played as many times as one wishes and the total score of the game is defined as the sum of points received after successive plays. It is observed that every integer x \geq1986 can be obtained as the total score whereas 1985 and 663 cannot. Determine a and b.