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: Time Limit Exceeded)

"use strict";
function main(input) {
  let kari = input[0].trim().split(" ");
  let n = parseInt(kari[0]);
  let a = parseInt(kari[1]);
  let b = parseInt(kari[2]);

  let bunbo = 1;
  let bunshi = 1;

  let sum = 0;
  for(let i=1;i<n+1;i++){
    bunshi *= (n+1-i);
    bunbo *= i;
    if(i!==a && i!==b){
      sum += (bunshi/bunbo);
    }
  }
  console.log(sum%(Math.pow(10,9)+7));
}
main(require('fs').readFileSync('/dev/stdin', 'utf8').trim().split("\n"));