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)

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

def comb(n, x):
    numerator = 1
    for i in range(n - x + 1, n + 1):
        numerator = numerator * i % mod
    denominator = 1
    for j in range(1, x + 1):
        denominator = denominator * j % mod
    d = pow(denominator, mod - 2, mod)
    return numerator * d
print((pow(2, n, mod) - comb(n, a) - comb(n, b) - 1) % mod)