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";
const factorial = num => {
  let number = 1;
  for (let i = 1; i <= num; i++) {
    number *= i;
  }
  return number;
};
function Main(input) {
  input = input.split(" ").map(Number);
  let total = 0;
  for (let i = 1; i <= input[0]; i++) {
    if (input[1] === i || input[2] === i) continue;
    total += factorial(input[0]) / (factorial(i) * factorial(input[0] - i));
  }
  console.log(total % (Math.pow(10, 9) + 7));
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));