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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input) {
	var tmp = input.split(" ");
	var n = parseInt(tmp[0], 10);
	var a = parseInt(tmp[1], 10);
	var b = parseInt(tmp[2], 10);
	var mod = Math.pow(2, 32)%1000000007;
	var mod32 = Math.floor(n/32);
	var ama32 = n%32;
	var ans = mod*mod32;
	ans += Math.pow(2, ama32);
    if(ans >= 1000000007){
      ans = ans%1000000007;
    }
	console.log(ans);
	var ma = 1;
	var ma2 = 1;
	var mb = 1;
	var na = n;
	var an = a;
	for(var i=0; i<a; i++){
    	ma *= na;
    	ma2 *= an;
    	if(ma%ma2 == 0){
        	ma = ma/ma2;
        	ma2 = 1;
        }
    	na--;
    	an--;
    	if(ma >= 1000000007){
           ma = ma%1000000007;
        }
    }
	na = n;
	an = b;
	var mb2 = 1;
	for(var i=0; i<b; i++){
    	mb *= na;
    	mb2 *= an;
    	if(mb%mb2 == 0){
        	mb = mb/mb2;
        	mb2 = 1;
        }
    	na--;
    	an--;
    	if(mb >= 1000000007){
           mb = mb%1000000007;
        }
    }
	var anser = ans-1-ma-mb;
	for(var i=0; i>=0; i){
		if(anser < 0){
       		anser += 1000000007;
    	}else{
        	break;
        }
    }
	console.log(ma);
	console.log(mb);
	console.log(anser);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));