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 powmod b, e, m
	z = 1
	while 0 < e
		z = z*b%m if e&1 == 1
		b, e = b*b%m, e>>1
	end
	return z
end
def xgcd a, b
	x, y, u, v = 1, 0, 0, 1
	until b == 0
		q, a, b = a/b, b, a%b
		x, y, u, v = u, v, x-q*u, y-q*v
	end
	return a, x, y
end
def imod a, m
	d, x, = xgcd a, m
	return nil unless d == 1
	return 0<x ? x : x+m
end

(N,A,B),M = gets.split.map(&:to_i), 1000000007

a,b, = [N-A,A,N-B,B].sort
c,d = N-b+1,N-a+1
f = lambda{|x,y| x*y%M }

x = powmod 2,N,M
y = (d..N).inject(imod((2..a).inject(1,&f),M),&f)
z = (c...d).inject(imod((a+1..b).inject(1,&f),M),&f)*y%M
p (x-y+M-z+M-1)%M