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 (3.4.3) (judge verdict: Accepted)

x=input().split()
n=int(x[0])
a=int(x[1])
b=int(x[2])

def fast_expo(b,n,p):
    if n==0:
        return 1
    if n==1:
        return b%p
    if n%2==0:
        return fast_expo(((b%p)*(b%p))%p,n//2,p)
    else:
        return (b*fast_expo(((b%p)*(b%p))%p,n//2,p))%p
def combi(n,k,p):
    X=1
    Y=1
    for i in range(k):
        X=(X*(n-i))%p
        Y=(Y*(k-i))%p
    Z=fast_expo(Y,p-2,p)
    return (X*Z)%p

p=10**9+7
res=fast_expo(2,n,p)
res=(res-1)%p
res=(res-combi(n,a,p))%p
res=(res-combi(n,b,p))%p
print(res)