Let A[1 ...n] be an array of n elements. We assume that no two elements of A are equal and A is not sorted. Let M be another given number. Our goal is to find the largest element x in A such that the sum of the elements of A less than x is smaller than M (i.e., Σ_{a ∈ A, a < x} a < M). We assume that the sum of all elements of A is larger than M. For example, suppose A contains seven numbers: {4, 5, 2, 3, 6, 8, 1}, and M = 10. Then, the largest such number x we are looking for is 4. Design an O(n) time algorithm for the problem by using the Prune-and-Search technique.
