21.14 LAB: Binary Search Binary search can be implemented as a recursive algorithm. Each call makes a recursive call on one-half of the list the call received as an argument. Complete the recursive function binary_search() with the following specifications: 1. Parameters: o a list of integers o a target integer o lower and upper bounds within which the recursive call will search 2. Return value: o if found, the index within the list where the target is located o 1 if target is not found The algorithm begins by choosing an index midway between the lower and upper bounds. 1. If target nums[index] return index 2. If lower -- upper, return lower if target -- nums [lower] else -1 to indicate not found 3. Otherwise call the function recursively with half the list as an argument: o If nums [index] < target, search the list from index to upper o if nums [index] > target, search the list from lower to index The list must be ordered, but duplicates are allowed. Once the search algorithm works correctly, add the following to binary_search(): 4. Count the number of calls to binary_search(). anamMvee Đaymber of times when the target is ompared to an element of the list. Note: lower == upper should not be counted. Hint: Use a global variable to count calls and comparisons. The Input of the program consists of integers on one line followed by a target integer on the second. The template provides the main program and a helper function that reads a list from input. Ex: If the input is: 1 234 5 6789 the output is: recurs ions: comparisons: 3