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)

# mを法とするaの乗法的逆元
def modinv(a, mod=10**9+7):
  return pow(a, mod-2, mod)

# nCr mod m
# modinvが必要
# rがn/2に近いと非常に重くなる
def combination(n, r, mod=10**9+7):
  r = min(r, n-r)
  res = 1
  for i in range(r):
    res = res * (n - i) * modinv(i+1, mod) % mod
  return res

n, a, b = map(int, input().split())
MOD=10**9+7

# すべての組み合わせ = 2 ** n - 1
all_comb = 2 ** n - 1

NG_comb_a = combination(n, a)
NG_comb_b = combination(n, b)

ans = (all_comb - NG_comb_a - NG_comb_b) % MOD

print(ans)