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"

var mod = int64(1e9) + 7

func main() {
	var n, a, b int64
	fmt.Scanf("%d %d %d\n", &n, &a, &b)

	nways := power(2, n) - nChooseK(n, a) - nChooseK(n, b) - 1
	for nways < 0 {
		nways += mod
	}

	fmt.Printf("%d\n", nways%mod)
}

func nChooseK(n, k int64) int64 {
	ret := int64(1)
	f := int64(1)
	for i := int64(1); i <= k; i++ {
		ret = (ret * (n - i + 1)) % mod
		f = (f * i) % mod
	}
	return (ret * power(f, mod-2)) % mod
}

func power(a, b int64) int64 {
	ret := int64(1)
	for b > 0 {
		if b%2 != 0 {
			ret = (ret * a) % mod
		}
		b /= 2
		a = (a * a) % mod
	}
	return ret
}