Today, I get a problem.

Sum of greatest odd divisor of numbers in range $$$[a, b]$$$ with $$$a, b <= 10^9$$$

I found solution here : https://www.geeksforgeeks.org/sum-of-greatest-odd-divisor-of-numbers-in-given-range/

But I think the solution is not clear for the even number case.

Can find a better solution or more detailed explanation ?

Sorry, my english was bad.

Thanks you.