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 bit=require"bit"
local ffi=require"ffi"
local function int(x)return ffi.new("int64_t",x)end
local function printn(x)print(tonumber(x))end
local function for64(a,b,c)c=c or 1 local x=a return c<0 and function()local ret=x x=x+c return ret>=b and ret or nil end or function() local ret=x x=x+c return ret<=b and ret or nil end end
local MOD=int(1000000007)
local function add(a,b)return (a+b)%MOD end
local function sub(a,b)a=(a-b)%MOD return a<0 and a+MOD or a end
local function mul(a,b)return a*b%MOD end
local function pow(a,b)
	local ret=int(1)
	while(b>0)do
		if(b%2==1)then ret=mul(ret,a)end
		a=mul(a,a)
		b=b/2
	end
	return ret
end
local function inv(x)
	local a=x
	local b,u,v=int(MOD),int(1),int(0)
	repeat
		local t=a/b
		a,b=b,a-t*b
		u,v=v,u-t*v
	until(b==0)
	u=u%MOD
	return u<0 and u+MOD or u
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=int(1)
	for i in for64(n,n-k+1,-1) do
		ret=mul(ret,i)
	end
	for i in for64(2,k) do
		ret=div(ret,i)
	end
	return ret
end

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