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)

// ncrModせいぜい10^6とかだった気がするので無理
// これは悔しいですね クソが

package main
import "fmt"
func main(){
	var N, A, B int
	fmt.Scan(&N, &A, &B)
	MOD := int(1e9)	+ 7
  // repModP、「どっちも選ばない」を含むのでそれを-1
	ans := (repModP(2, N, MOD) - 1 - nCrModP(N, A, MOD) - nCrModP(N, B, MOD))%MOD
	if ans < 0{
		ans += MOD
	}
	fmt.Println(ans)
}

func repModP(a, n, mod int)int{
	if n==1{
		return a % mod
	}
	if n % 2 == 1{
		return a * repModP(a, n-1, mod) % mod
	}
	ret := repModP(a, n/2, mod) % mod
	ret = (ret * ret) % mod
	if ret < 0{
		ret += mod
	}
	return ret
}

func nCrModP(n, r, mod int)int{
	ret := 1
	for i:=n-r+1; i<=n; i++{
		ret *= i
		ret %= mod
	}
	for i:=2; i<=r; i++{
		ret *= repModP(i, mod-2, mod)
		ret %= mod
	}
	ret %= mod
	if ret < 0{
		ret += mod
	}
	return ret
}