Minimum Digit Sum 2

_This problem is similar to the problem "MNDIGSUM". The only differences are in the constraints and in the input format. In this problem the range for the base $B$ is $[2, R]$, the value of $n$ can be upto $10^{12}$ and the total number of queries is at most $300$. The differences are described in bold._ Let $f(n, B)$ be the sum of digits of the integer $n$ when written in base $B$. More formal