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: Accepted)

n,a,b=gets.split.map(&:to_i)
m=1000000007
f=[1]
1000000.times do |i|
  f << f[-1]*(i+1)%m
end
def mi(a,m)
  b,u,v=m,1,0
  while b>0
    t=a/b
    a-=t*b
    u-=t*v
    a,b,u,v=b,a,v,u
  end
  u%=m
  u+=m if u<0
  return u
end
nca=1
i=n
a.times do
  nca=nca*i%m
  i-=1
end
nca=nca*mi(f[a],m)%m
ncb=1
i=n
b.times do
  ncb=ncb*i%m
  i-=1
end
ncb=ncb*mi(f[b],m)%m
nl=[2]
30.times do
  nl << nl[-1]**2%m
end
i=0
nn=1
while n>0
  if n.odd?
    nn=nn*nl[i]%m
  end
  n/=2
  i+=1
end
puts (nn-1-nca-ncb)%m