Score : $400$ points

Problem Statement

Akari has $n$ kinds of flowers, one of each kind.

She is going to choose one or more of these flowers to make a bouquet.

However, she hates two numbers $a$ and $b$, so the number of flowers in the bouquet cannot be $a$ or $b$.

How many different bouquets are there that Akari can make?

Find the count modulo $(10^9 + 7)$.

Here, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet.

Constraints

• All values in input are integers.
• $2 \leq n \leq 10^9$
• $1 \leq a < b \leq \textrm{min}(n, 2 \times 10^5)$

Input

Input is given from Standard Input in the following format:

$n$ $a$ $b$

Output

Print the number of bouquets that Akari can make, modulo $(10^9 + 7)$. (If there are no such bouquets, print 0.)

4 1 3

7

In this case, Akari can choose $2$ or $4$ flowers to make the bouquet.

There are $6$ ways to choose $2$ out of the $4$ flowers, and $1$ way to choose $4$, so there are a total of $7$ different bouquets that Akari can make.

1000000000 141421 173205

34076506

Print the count modulo $(10^9 + 7)$.