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 readInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return i
}

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

func readInt64() int64 {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return int64(i)
}

func readfloat64() float64 {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return float64(i)
}

func abs(a int) int {
	if a < 0 {
		return a * -1
	}
	return a
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

const Mod = 1000000007

func ModComb(n, k int) int {
	if k == 0 {
		return 1
	}
	x, y := n, k
	for i := 1; i < k; i++ {
		x = x * (n - i) % Mod
		y = y * (k - i) % Mod
	}
	inv := ModInv(y)
	return x * inv % Mod
}

func ModFact(x int) int {
	fact := 1
	for i := 1; i <= x; i++ {
		fact = fact * i % Mod
	}
	return fact
}

func ModInv(x int) int {
	return ModPow(x, Mod-2)
}

func ModPow(a, n int) int {
	res := 1
	for n > 0 {
		if n%2 != 0 {
			res = res * a % Mod
		}
		a = a * a % Mod
		n /= 2
	}
	return res
}

func main() {
	sc.Split(bufio.ScanWords)
	n, a, b := readInt(), readInt(), readInt()

	ans := ModPow(2, n)

	ans -= 1

	if ans -= ModComb(n, a); ans < 0 {
		ans += Mod
	}

	if ans -= ModComb(n, b); ans < 0 {
		ans += Mod

	}
	fmt.Println(ans)
}