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)

#!/usr/bin/env python3
from functools import reduce
from operator import mul

mod = 10**9 + 7


def cmb(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    over = reduce(lambda a, b: a * b % mod, range(n, n - r, -1))
    under = reduce(lambda a, b: a * b % mod, range(1, r + 1))
    return over * pow(under,mod-2,mod)


n, a, b = map(int, input().split())
print((pow(2, n, mod) - 1 - cmb(n, a) - cmb(n, b)) % mod)