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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
)

const mod = 1000000007

func pow(x, y int) int {
	if y == 0 {
		return 1
	} else if y%2 == 0 {
		x2 := pow(x, y/2)
		return x2 * x2 % mod
	} else {
		return x * pow(x, y-1) % mod
	}
}

func cmb(x, y int) int {
	if y > x {
		return 0
	}

	nu, de := 1, 1
	for i := 0; i < y; i++ {
		nu = nu * (x - i) % mod
		de = de * (i + 1) % mod
	}
	return nu * pow(de, mod-2) % mod
}

func main() {
	var n, a, b int
	fmt.Scan(&n, &a, &b)

	ans := pow(2, n) - 1
	ans -= cmb(n, a)
	ans -= cmb(n, b)
	ans = (ans%mod + mod) % mod
	fmt.Println(ans)
}