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 PyPy3 (2.4.0) (judge verdict: Accepted)

n,a,b=map(int,input().split())
mod=10**9+7

def cmb(n, r,mod):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    #X//Y
    X=1
    Y=1
    for i in range(r):
        X*=(n-i)
        X%=mod
        Y*=(i+1)
        Y%=mod
        
    inv=pow(Y,mod-2,mod)
    return (X*inv)%mod
        
        


allp=pow(2,n,mod)-1
ans=(allp-cmb(n,a,mod)-cmb(n,b,mod))%mod
if n==2:
    ans=0

print(ans)