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 (1.14.1) (judge verdict: Accepted)

// フェルマーの小定理
package main

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

const (
	m = 1000000007
)

func mpow(x, y int) int {
	result := 1
	for y != 0 {
		if y&1 == 1 {
			result *= x
			result %= m
		}
		x *= x
		x %= m
		y >>= 1
	}
	return result
}

func mcomb(n, k int) int {
	a := 1
	b := 1
	for i := 0; i < k; i++ {
		a *= n - i
		a %= m
		b *= i + 1
		b %= m
	}
	return a * mpow(b, m-2) % m
}

func main() {
	n := readInt()
	a := readInt()
	b := readInt()

	result := mpow(2, n) - 1
	result -= mcomb(n, a)
	result += m
	result %= m
	result -= mcomb(n, b)
	result += m
	result %= m
	fmt.Println(result)
}

const (
	ioBufferSize = 1 * 1024 * 1024 // 1 MB
)

var stdinScanner = func() *bufio.Scanner {
	result := bufio.NewScanner(os.Stdin)
	result.Buffer(make([]byte, ioBufferSize), ioBufferSize)
	result.Split(bufio.ScanWords)
	return result
}()

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

func readInt() int {
	result, err := strconv.Atoi(readString())
	if err != nil {
		panic(err)
	}
	return result
}