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)

def comb(n, r, mod):
    r = min(r, n-r)
    mol = 1
    for i in range(n-r+1, n+1):
        mol = (mol * i) % mod
    deno = 1
    for i in range(1, r+1):
        deno = (deno * i) % mod
    ret = mol * pow(deno, mod-2, mod) % mod
    return ret

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

P = 10**9+7

nCa = comb(n, a, P)
nCb = comb(n, b, P)

ans = (pow(2,n,P) -1 - nCa - nCb + 2*P)%P
print(ans)