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: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

var (
	factorialMemo []int
)

func repeatedSquaring(n, p, m int) int {
	if p == 0 {
		return 1
	}
	if p%2 == 0 {
		t := repeatedSquaring(n, p/2, m)
		return t * t % m
	}
	return n * repeatedSquaring(n, p-1, m) % m
}

func main() {
	var n, a, b int
	fmt.Scan(&n, &a, &b)

	divisor := int(math.Pow10(9) + 7)
	all := repeatedSquaring(2, n, divisor) - 1

	for _, k := range []int{a, b} {
		x := 1
		y := 1
		for i := 0; i < k; i++ {
			x = x * (n - i) % divisor
			y = y * (i + 1) % divisor
		}

		r := x * repeatedSquaring(y, divisor-2, divisor) % divisor
		// fmt.Println(all, a, b, x, y, r, divisor)
		all -= r
	}

	if all < 0 {
		all += divisor
	}

	fmt.Println(all)
}