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)

nn, aa, bb = gets.chomp.split(" ").map(&:to_i)
$BIGMOD = (10**9) + 7
def nCk(n,k)
	b = (1..k).inject(1){|p, c| p * c % $BIGMOD}
	a = (0..k-1).inject(1){|p, c| p * (n - c) % $BIGMOD}
  a * Inv(b) % $BIGMOD
end

def nPk(n,k)
	return Fact(n) / Fact(n-k) % $BIGMOD
end

def Fact(n)
  (1..n).inject(1) { |r, i| (r * i) % $BIGMOD }
end

def Inv(n)
  PowPow(n, $BIGMOD - 2) % $BIGMOD
end

def PowPow(x, n)
  return 1 if n == 0
	return PowPow(x**2  % $BIGMOD, n / 2) if n.even?
  return PowPow(x, n-1) * x  % $BIGMOD 
end

ngo = PowPow(2, nn) - 1
ngo -= nCk(nn, aa)
ngo -= nCk(nn, bb)
puts ngo % $BIGMOD