TW-TST 1993 Problem 5

Assume $A=\{a_{1},a_{2},...,a_{12}\}$ is a set of positive integers such that for each positive integer $n \leq 2500$ there is a subset $S$ of $A$ whose sum of elements is $n$ . If $a_{1}<a_{2}<...<a_{12}$ , what is the smallest possible value of $a_{1}$ ?