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)

MOD = 1000000007

def conv(a,b)
  if b > a/2
    b = a - b
  end
  ans = 1
  div = 1
  b.times do |i|
    ans *= a - i
    ans %= MOD
    div *= (i+1)
    div %= MOD
  end
  ans = ans * pow(div, MOD-2)
  ans % MOD
end

def pow(x,n)
  if n == 0
    1
  elsif n % 2 == 0
    pow(x*x%MOD, n/2) % MOD
  else
    x * pow(x, n-1) % MOD
  end
end

n,a,b=gets.chomp.split(" ").map(&:to_i)

all = (pow(2,n) - 1) % MOD
if a > n/2
  a = n - a
end
if b > n/2
  b = n - b
end

all = all - conv(n,a) - conv(n,b)
all %= MOD

puts all