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)

function K_kuri(N,P,M)
    ( P ≤ 0 )  && return 1
    ( P%2==0 ) && return K_kuri(N,P÷2,M)^2 % M
    N*K_kuri(N,P-1,M) % M
end

function CmbMod(a,b,M)
    A=B=1
    for i in 1:b
        A*=(a-i+1)%M
        B*=K_kuri(i,M-2,M)
        A%=M
        B%=M
    end
    A*B%M
end

input=split(readline())
MOD=10^9+7
N,a,b=map(x->parse(Int,x),input)

print((K_kuri(2,N,MOD)-1-CmbMod(N,a,MOD)-CmbMod(N,b,MOD)+3MOD)%MOD)