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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func stringLineScan() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, 1000000009)
	sc.Split(bufio.ScanWords)
	n, _ := strconv.Atoi(stringLineScan())
	a, _ := strconv.Atoi(stringLineScan())
	b, _ := strconv.Atoi(stringLineScan())
	d := 1000000007
	x := repeatPaw(2, n, d) - 1
	cal, car, cbl, cbr := 1, 1, 1, 1
	for i := 1; i <= a; i++ {
		cal *= n - i + 1
		car *= i
		cal %= d
		car %= d
	}
	for i := 1; i <= b; i++ {
		cbl *= n - i + 1
		cbr *= i
		cbl %= d
		cbr %= d
	}
	ans := (x - cal*modinv(car, d)%d - cbl*modinv(cbr, d)%d) % d
	if ans < 0 {
		ans += d
	}
	fmt.Println(ans)
}
func modinv(a, m int) int {
	b, u, v := m, 1, 0
	for {
		t := a / b
		a -= t * b
		u -= t * v
		a, b, u, v = b, a, v, u
		if b == 0 {
			break
		}
	}
	u %= m
	if u < 0 {
		u += m
	}
	return u
}
func repeatPaw(x, y, d int) int {
	if y == 1 {
		return x
	} else {
		z := repeatPaw(x, y/2, d)
		if y%2 == 0 {
			return z * z % d
		} else {
			return z * z % d * x % d
		}
	}
}