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 PyPy2 (5.6.0) (judge verdict: Accepted)

import math


mod=10**9+7

def ncr(n,r):
	res=1
	for i in range(1,r+1):
		res=(res*(n-r+i))%mod
		inv=pow(i,mod-2,mod)
		res=(res*inv)%mod
	return res

n,a,b=map(int,raw_input().split())
p=pow(2,n,mod)
p=(p-1+mod)%mod
p=(p-ncr(n,a)+mod)%mod
p=(p-ncr(n,b)+mod)%mod
print p