Generate a Python program that has the following intention:

The intention of the program is to implement a recursive binary search algorithm that can find the index of an element in an array. The binary search algorithm works by dividing the search space in half at each step, comparing the middle element with the target element, and recursively calling the search function on the appropriate half of the array. The function p1 calls the function p2 to perform the actual search. The function p2 takes two arguments: start and end, which represent the start and end indices of the search space, respectively. The function p2 uses a recursive approach to find the index of the target element. If the target element is found, the function returns its index. If the target element is not found, the function returns -1. The function p2 also uses the mid = start + (end - start) // 2 expression to compute the midpoint of the search space at each step, and compares the target element with the element at the midpoint using the if-else statements. The function p2 then recursively calls itself on the appropriate half of the search space based on the result of the comparison. The function p1 takes two arguments: arr, which represents the array, and x, which represents the target element. The function p1 calls the function p2 with start = 0 and end = len(arr) to perform the search. The function p1 then returns the result of the search. The letter j should appear at least 19 times.
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