Consider the following problem. Given a sorted array a of consisting of distinct integers and an integer T, determine if there exist two integers in the array (possibly the same integer) whose sum equals T. Consider the following algorithm: Input: Array a, Integer T. left 0; right while (left T) right--; return false; Show that the above program is correct by proving the following: At the start of the ith iteration the following conditions hold: left < right If there exist indices and j such that a[] + a[j] equals T, then left