Problem:
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.)

Sample Input 1

4 1 3

Sample Output 1

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.

Sample Input 2

1000000000 141421 173205

Sample Output 2

34076506

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

Solution in Julia (0.5.0) (judge verdict: Accepted)

parseInt(s)=parse(Int,s)
MOD=10^9+7
N,a,b=parseInt.(split(readline()))

f=let
    A=1
    for i in 1:a
        A*=((N-i+1)*invmod(i,MOD))%MOD
        A%=MOD
    end
    B=A
    for i in a+1:b
        B*=((N-i+1)*invmod(i,MOD))%MOD
        B%=MOD
    end
    (powermod(2,N,MOD)-1-A-B+3MOD)%MOD
end

print(f)