Given the following recursive binary search algorithm for finding an element in a sorted array of integers: int recursivebinarysearch(int[] array, int target, int left, int right){ if (left > right) return -1; int middle = (left + right) / 2; if (array[middle] == target) return middle; if (array[middle] > target) return recursivebinarysearch(array, target, left, middle - 1); return recursivebinarysearch(array, target, middle + 1, right); }assume n is the length of the array. find the initial condition and recurrence equation that expresses the execution time for the worst case of this algorithm and then solve that recurrence.