The Reminder to Expect

Do you know Trevor Philips? Well he is a mad guy who gets mad at everything. Recently he got mad at reminders because some shopkeeper kept them as changes.

Today Trevor chooses to spend no more than $N$ dollars. So he is wondering what would be the expected value of the reminder from dividing $x$ by $y$ if he chose $x$ and $y$ randomly and independently from 1 to $N$. And he is also confused about the number $N$. So now he wants to know the sum of such expected values for all $N$ from 1 to $M$.

Well now he is too angry to do the math, so he hired you.

Input

The input contains only one integer — $M$ ($1 ≤ M ≤ 10^6$)

Output

Print one number expressing the sum of the expected values in following format — If the answer is $\frac{P}{Q}$, then print the number $P \times Q^{−1} \space \text{modulo} \space 10^9+7$, where $Q^{-1}$ denotes the multiplicative inverse of $Q$ modulo $10^9+7$.

Samples

Input	Output
1	0

Input	Output
2	250000002

Input	Output
10	94129043