Jo loves his teammate Ky's rick and roll! But he more than loves counting.
Jo thinks, for two numbers $n$ and $d$ ( $d$ is a factor of $n$ ), $d \in Good_n$ if and only if the prime factor set of $d$ $\textbf{equals}$ to that of $n$. That is, $Good_n=\lbrace d\mid n\bmod d=0\wedge \forall p\in Prime\to (d\bmod p=0\leftrightarrow n\bmod p=0)\rbrace $.
For example, $Good_{12}=\lbrace 6, 12\rbrace $ , since the factors of $12$ are $\lbrace 1, 2, 3, 4, 6, 12\rbrace $. $\lbrace 2, 3\rbrace $ are prime factors of $12$, so all its factors of their good factors must contain prime factors $2, 3$. Therefore, only $6, 12$ satisfy the condition.
For a number $n$, Jo will select a factor $d$ randomly from $Good_n$ with equal possibility. if $d=n$, then the rich Jo will pay you $n$ yuan as reward. Otherwise, you will gain nothing.
Ky, the man who treats money as dirt, wants to choose an integer from $[1, M]$ randomly for Jo's game. Help Ky calculate the expectation of money he can get.