Bunty recently learned about the significance of $d(n)$, the smallest prime divisor of $n$, through which he can quickly extract prime factorisations of numbers!

He sits down and drafts an interesting sequence of integers where the integers are bound between the values $2$ to $1,000,000$. To him, a sequence $a_i$ is interesting if $a_i$ is strictly increasing and the corresponding sequence $d(a_i)$ is also strictly increasing.

Bunty attempts to write all interesting sequences but soon realises that there are too many of them. Can you, the algorithmist, count the number of interesting sequences modulo $10^9 + 7$?