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 Python (3.8.2) (judge verdict: Accepted)

n,a,b = map(int,input().split())

mod = 10**9+7

all_combi = pow(2,n,mod)




p = 1
q = 1

for i in range(b):
    
    p *= n-i
    p %= mod
    q *= i+1
    q %= mod
    
    if i==a-1:
        nca = p * pow(q,-1,mod) % mod
        
    if i==b-1:
        ncb = p * pow(q,-1,mod) % mod

        
ans = all_combi -nca -ncb -1
ans %= (10**9+7)
    
print(ans)