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 PyPy3 (7.3.0) (judge verdict: Accepted)

from math import *
def modpow(a,n,m):
  res=1
  while n>0:
    if n&1:res=res*a%m
    a=a*a%m
    n//=2
  return res
n,a,b=map(int,input().split())
mod=10**9+7
ans=modpow(2,n,mod)-1
na=1
nb=1
for i in range(a):
  na*=(n-i)%mod
  na%=mod
fa=1
for i in range(1,a+1):
  fa*=i
  fa%=mod
na*=modpow(fa,mod-2,mod)
for i in range(b):
  nb*=(n-i)%mod
  nb%=mod
fb=1
for i in range(1,b+1):
  fb*=i
  fb%=mod
nb*=modpow(fb,mod-2,mod)
print((ans-nb-na)%mod)