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"
)

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

	nCi := pow(2, n) - 1
	nCa := comb(n, a)
	nCb := comb(n, b)

	ans := sub(nCi, add(nCa, nCb))
	fmt.Println(ans)
}

const mod int = 1e9 + 7

func pow(n, k int) int {
	if k == 0 {
		return 1
	} else if k%2 == 1 {
		return pow(n, k-1) * n % mod
	} else {
		t := pow(n, k/2)
		return t * t % mod
	}
}

func comb(n, r int) int {
	nu := 1
	for i := 0; i < r; i++ {
		nu = mul(nu, n-i)
	}

	de := 1
	for i := 1; i <= r; i++ {
		de = mul(de, i)
	}

	return div(nu, de)
}

func add(a, b int) int {
	return (a + b) % mod
}

func sub(a, b int) int {
	return (a + mod - b) % mod
}

func mul(a, b int) int {
	return a % mod * b % mod % mod
}

func div(a, b int) int {
	return mul(a, pow(b, mod-2))
}