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: Accepted)

n, a, b = map(int, input().split())


mod = 1000000007

inv = [1] * 222222

# 0 = a * MOD/a + MOD % a
# a*MOD/a = -MOD%a
# a = -MOD%a * inv[MOD/a]
# inv[a] = -inv[MOD%a] * MOD/a
for i in range(2, 222222):
    inv[i] = -inv[mod % i] * (mod // i)
    inv[i] %= mod
    
def comb(n, a):
    res = 1
    for i in range(a):
        res *= n-i
        res *= inv[i+1]
        res %= mod
    return res

ans = pow(2, n, mod) - 1 - comb(n, a) - comb(n, b)

ans %= mod
if ans < 0:
    ans += mod

print(ans)