You have a set of dice, where each die has a number of sides that corresponds to a prime number less than $10^7$. For example, the set includes dice with $2, 3, 5, 7,$ and other prime numbers of sides.

A die is chosen randomly from this set. After selecting the die, you keep tossing it until every face of the die has appeared at least once. For instance, for a $3$-sided die, you might toss the die multiple times until you have seen all three faces $(1, 2,$ and $3)$ at least once.

The sequence of tosses could look something like $2, 1, 1, 2, 3$, which means it took $5$ tosses to see all three faces.

Your task is to find the expected number of tosses required to see all faces of the die you picked. Report the result $modulo$ $10^9 + 7.$