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"
	"io"
	"os"
	"strconv"
)

var sc *bufio.Scanner

const bufferSize = 1024

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

var production bool

func debugf(format string, v ...interface{}) {
	if !production {
		fmt.Printf(format, v...)
	}
}

func mpow(x, n, M uint64) uint64 {
	ans := uint64(1)
	for n != 0 {
		if n&1 == 1 {
			ans = ans * x % M
		}
		x = x * x % M
		n = n >> 1
	}
	return ans
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func answer(reader io.Reader, writer io.Writer) {
	sc = bufio.NewScanner(reader)
	buf := make([]byte, bufferSize)
	sc.Buffer(buf, 1e+7)
	sc.Split(bufio.ScanWords)
	n := nextInt()
	a := nextInt()
	b := nextInt()

	mod := int(1e9) + 7
	ans := int(mpow(uint64(2), uint64(n), uint64(mod))) - 1

	debugf("%v\n", ans)
	nume := 1
	deno := 1
	for i := 0; i < min(a, b); i++ {
		nume *= n - i
		nume %= mod
		deno *= (i + 1)
		deno %= mod
	}
	ans -= int(uint64(nume) * mpow(uint64(deno), uint64(mod-2), uint64(mod)) % uint64(mod))
	debugf("%v\n", ans)
	if ans < 0 {
		ans += mod
	}
	for i := min(a, b); i < max(a, b); i++ {
		nume *= n - i
		nume %= mod
		deno *= (i + 1)
		deno %= mod
	}
	ans -= int(uint64(nume) * mpow(uint64(deno), uint64(mod-2), uint64(mod)) % uint64(mod))
	debugf("%v\n", ans)
	if ans < 0 {
		ans += mod
	}

	_, _ = fmt.Fprintf(writer, "%d", ans)
}

func main() {
	production = true
	answer(os.Stdin, os.Stdout)
}