Give an $O(nt)$ algorithm for the following task.

Input: A list of $n$ positive integers $a_1,a_2,$dots,$a_n$; a positive integer $t.$

Question: Does some subset of the $a_i\text{'}$s add up to t$?($You can use each $a_i$ at most once.

$($Hint: Look at subproblems of the form "does a subset of $\{a_1,a_2,$dots,$a_i\}$ add up to s$?")$