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 (2.3.3) (judge verdict: Accepted)

def xgcd(a, b)
  x=xx=yy=q = 1
  y = 0
  x = a = 0  if b == 0
  while b > 0
    xx -= q*x; yy -= q*y
    q,a = a.divmod b
    return [b,xx,yy]  if a == 0
    x -= q*xx; y -= q*yy
    q,b = b.divmod a
  end
  [a,x,y]
end
N,A,B = gets.split.map &:to_i
P = 10**9+7
n,s,PP = 1,2,P<<2
30.times {|i| n*=s if N[i]>0; s*=s; s%=P if s>P;n%=P if n>PP}
a,b = [A,B].map{|r| N < r+r ? N-r : r}.sort
s=t=u = 1
f = proc {|i| t,u = [t*(N+1-i), u*i].map!{|x| x>P ? x%P : x} }
[[1,a],[a+1,b]].each {|x,y| x.upto(y ,&f); s += t*xgcd(u,P)[1]%P }
p (n-s) % P