Maybe this is quite simple, but I am having some trouble how to do this reduction. I want to reduce Subset Sum to Almost Subset Sum.
Subset Sum: given a set of positive integers $A=\{a_1,a_2, \dots,a_n\}$ and an integer $M$, decide if there is a subset of $A$ with a sum equal to $M$.
Almost Subset Sum:
Input: a set of positive integers $A=\{a_1,a_2, \dots,a_n\}$, and a positive integer $M$.
Goal: decide whether there is a subset of $A$ with sum $S$ such that $|M −S| < d$ where $d = ⌊\log M ⌋$?
