Maximise Set Bits

Let $f(X)$ denote the number of set bits in $X$. Given integers $N$ and $K$, construct an array $A$ of length $N$ such that: - $0 \leq A_i \leq K$ for all $(1 \le i \le N)$; - $\sum_{i=1}^{N} A_i = K$ Over all such possible arrays, find the **maximum** value of $\sum_{i=1}^{N} f(A_i)$. ### Input - The first line of input contains a single integer $T$ - the number of test cases. The description