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 int64
	const M = 1000000007

	fmt.Scan(&n)
	fmt.Scan(&a)
	fmt.Scan(&b)

	answer := modpow(2, n, M) - 1

	ca, cb := int64(1), int64(1)
	for i := int64(0); i < a; i++ {
		ca = ca * (n - i) % M * modinv(1 + i, M) % M
	}
	for i := int64(0); i < b; i++ {
		cb = cb * (n - i) % M * modinv(1 + i, M) % M
	}
	answer = (answer - ca - cb + 2 * M) % M
	fmt.Println(answer)
}

func modpow(a int64, n int64, m int64) int64 {
	if n == 0 {
		return 1
	}
	tmp := modpow(a, n / 2, m)
	if n % 2 == 0 {
		return tmp * tmp % m
	}
	return tmp * tmp % m * a % m
}

func modinv(a int64, m int64) int64 {
	return modpow(a, m - 2, m)
}