Decide target via subsequence plus/multiply expression

Given a sequence of positive 32-bit integers A and an integer target, determine whether there exists a subsequence of A (preserving order, using each element at most once) and a placement of '+' and '*' operators between the chosen numbers such that, with equal precedence and strict left-to-right evaluation, the resulting value equals target. For example, for A = [1, 9, 8, 7, 10, 3, 1] and target = 25, one valid expression is 8*3+1. Implement a function that returns true/false and, if true, also returns one valid expression. Discuss: ( 1) a backtracking search that enforces left-to-right evaluation without normal operator precedence; ( 2) pruning heuristics (e.g., stop when partial value already exceeds reasonable bounds, avoid repeating equivalent states, and early termination rules); ( 3) a reverse search from the target using subtraction and division where subtraction continues only if the remainder stays >= 0 and division only when the current target is exactly divisible by the chosen number—explain correctness conditions and ordering; ( 4) time and space complexity, and worst-case behavior; ( 5) dealing with 32-bit overflow for intermediate results and other edge cases.