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)

def modpow(a, n, p):
    if n == 1:
        ans = a % p
    else:
        if n % 2 == 0:
            ans = (modpow(a, n // 2, p) ** 2) % p
        else: # n % 2 == 1
            ans = (a * (modpow(a, n // 2, p) ** 2)) % p

    return ans

p = 10 ** 9 + 7
n, a, b = [int(x) for x in input().split()]

tot = modpow(2, n, p)

Xa, Ya = 1, 1
for i in range(a):
    Xa = (Xa * (n - i)) % p
    Ya = (Ya * (i + 1)) % p
Za = modpow(Ya, p - 2, p)
nCa = (Xa * Za) % p

Xb, Yb = 1, 1
for i in range(b):
    Xb = (Xb * (n - i)) % p
    Yb = (Yb * (i + 1)) % p
Zb = modpow(Yb, p - 2, p)
nCb = (Xb * Zb) % p

ans = (tot - nCa -nCb - 1) % p

print(ans)