Binary Expansion Sum

Let us consider the binary expansion of a number $n$. Every number can be represented in the form $$n=\sum{2^{p_i}}$$For example: - $5=2^2+2^0$ - $12=2^3+2^2$ - $15=2^3+2^2+2^1+2^0$ and so on. Let us define a function $f(n)$ such that $$f(n)=\sum{f(p_i)}$$ with base cases - $f(0)=a$ - $f(1)=b$ You are given $n$, $a$, and $b$. Compute $f(n)$. ###Input: - First line will contain $T$, number of t