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 LuaJIT (2.0.4) (judge verdict: Accepted)

local MOD=1000000007
local function add(a,b)return (a+b)%MOD end
local function sub(a,b)return (a-b)%MOD end
local function mul_(a,b)
	local ret=0
	while(b>0)do
		if(b%2==1)then ret=(ret+a)%MOD end
		a=(a+a)%MOD
		b=math.floor(b*.5)
	end
	return ret
end
local function mul(a,b)
	return a<b and mul_(b,a)or mul_(a,b)
end
local function pow(a,b)
	local ret=1
	while(b>0)do
		if(b%2==1)then ret=mul(ret,a)end
		a=mul(a,a)
		b=math.floor(b*.5)
	end
	return ret
end
local function inv(x)
	local a=x
	local b,u,v=MOD,1,0
	repeat
		local t=math.floor(a/b)
		a,b=b,a-t*b
		u,v=v,u-t*v
	until(b==0)
	return u%MOD
end
local function div(a,b)return mul(a,inv(b))end
local function C(n,k)
	if(n<k)then return 0 end
	local ret=1
	for i=n,n-k+1,-1 do
		ret=mul(ret,i)
	end
	for i=2,k do
		ret=div(ret,i)
	end
	return ret
end

n=io.read"*n"
a=io.read"*n"
b=io.read"*n"
print(sub(sub(sub(pow(2,n),C(n,a)),C(n,b)),1))