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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	ans,n,a,b,mo:int64;
function p(a,b:int64):int64;
begin
	if b=0 then p:=1 else if b mod 2=0 then p:=p(a*a mod mo,b div 2) else p:=p(a,b-1)*a mod mo;
end;
function C(k:int64):int64;
var x,y:int64;i:Longint;
begin
	x:=1;
	y:=1;
	for i:=1 to k do begin
		x:=x*(n-i+1)mod mo;
		y:=y*i mod mo;
	end;
	C:=x*p(y,mo-2)mod mo;
end;
begin
	read(n,a,b);
	mo:=1000000007;
	ans:=p(2,n)-1-c(a)-c(b);
	ans:=(ans mod mo+mo)mod mo;
	writeln(ans);
end.