Derive Dietz's formula for the average of two unsigned integers.

In a world where digital images are represented as a grid of pixels, each pixel having a color intensity value, a team of image processing experts are tasked with developing an algorithm to calculate the average color intensity of two adjacent pixels. The experts stumble upon an old manuscript describing Dietz's formula, which claims to provide an efficient method for calculating the average of two unsigned integers. The team is intrigued and decides to derive the formula to improve their image processing techniques.

Examples
Input: "test_input_1"
Output: "output_1"
Hints

Derive Dietz's formula for the average of two unsigned integers.

In a world where digital images are represented as a grid of pixels, each pixel having a color intensity value, a team of image processing experts are tasked with developing an algorithm to calculate the average color intensity of two adjacent pixels. The experts stumble upon an old manuscript describing Dietz's formula, which claims to provide an efficient method for calculating the average of two unsigned integers. The team is intrigued and decides to derive the formula to improve their image processing techniques.