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)

import functools, operator


def read():
    N, A, B = list(map(int, input().strip().split()))
    return N, A, B


table = []

def solve(N, A, B, MOD=10**9+7):
    n = (pow(2, N, MOD) + MOD - 1) % MOD
    a = nCk(N, A, MOD)
    b = nCk(N, B, MOD)
    return (n + MOD + MOD - a - b) % MOD


def factorial(n, MOD=10**9+7):
    return functools.reduce(lambda x, y: (x*y) % MOD, range(1, n+1))



def modinv(n, p):
    """
    逆元のmod pを求める
    """
    if n >= p:
        raise ValueError('p must be larger than n')
    return pow(n, p-2, p)


def nCk(n, k, MOD=10**9+7):
    r = 1
    kmin = min(k, n-k)
    for i in range(1, kmin+1):
        r = (r * modinv(i, MOD)) % MOD
    for i in range(n-kmin+1, n+1):
        r = r * i % MOD
    return r

if __name__ == '__main__':
    inputs = read()
    print("{}".format(solve(*inputs)))