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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

n,a,b=gets.split.map(&:to_i)
m=1000000007
# 2^n-1-nCa-nCb
nca=1
i=n
a.times do
  nca=nca*i
  i-=1
end
i=a
a.times do
  nca=nca/i
  i-=1
end
ncb=1
i=n
b.times do
  ncb=ncb*i
  i-=1
end
i=b
b.times do
  ncb=ncb/i
  i-=1
end
puts (2**n-1-nca-ncb)%m