Let S be a set of n positive integers each of which is less than k$.$ You are given set S and a natural number b$,$ such that b $<$ nk and goal is to check if there exist a subset A of S such that the addition of all the elements in the subset A is b$.$ Give an algorithm which has time complexity bounded above by O$(($nk$)^$ n $*$ c$)$ for an absolute constant c$.$ Give detailed pseudo$-$code and the complexity analysis. $($Hint: Note similarity with coin change problem$)$