Sheldon Cooper and his family will participate in a Secret Santa game, which will take place at the town church. Pastor Jeff wrote down the name of each of the $$$n$$$ people who will participate and then randomly distributed a piece of paper to each person. After that, each person must buy a gift for the person whose name is on the paper they received.

Sheldon calculated and told the pastor that there is a high chance that someone will draw their own name. In that case, they would have to buy a gift for themselves, and the game would be boring!

Jeff does not trust Sheldon and asked you to create a program that calculates the probability that at least one person draws their own name. It is guaranteed that the answer can be expressed as a fraction $$$\frac{a}{b}$$$. You should print $$$a \cdot b^{-1}\ mod \ M$$$, where $$$M = 10^9 + 7$$$. It can be shown that under these constraints $$$b \neq 0\ mod \ M$$$.