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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

mod = 10**9+7
n,a,b = [int(i) for i in input().split()]
k = min(n,2*(10**5))
def pow_k(x, n):
    if n == 0:
        return 1

    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        n //= 2

    return (K * x - 1) % mod
def modinv(a, mod):
    return pow(a, mod-2, mod)
def combination_list(n, mod):
    lst = [1]
    for i in range(1, k+1):
        lst.append(lst[-1] * (n+1-i) % mod * modinv(i, mod) % mod)
    return lst
ans = pow_k(2,n)
cmb = combination_list(n,mod)
ans %= mod
ans -= cmb[a]
if ans < 0:
    ans += mod
ans -= cmb[b]
if ans <0:
    ans += mod
print(ans)