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 Python (3.4.3) (judge verdict: Runtime Error)

import sys
from operator import mul
from functools import reduce
sys.setrecursionlimit(9**9)
def P(a,n,p):
  bi=str(format(n,"b"))
  res=1
  for i in range(len(bi)):
    res=(res*res)%p
    if bi[i]=="1":
      res=(res*a)%p
  return res
n,a,b=map(int,input().split())
a,b=min(a,n-a),min(b,n-b)
m=10**9+7
N=min(n,2*10**5)
inv=[0 for _ in range(max(a,b))]
inv[1]=1
if max(a,b)>1:
  for i in range(2,max(a,b)):
    inv[i]=m-inv[m%i]*(m//i)%m
def C(n,r,a):
  for i in range(r):
    a=a*(n-i)*inv[r-i-1]%m
  return a
A,B=C(n,a,1),C(n,b,1)
print((P(2,n,m)-int(A)-int(B)-1+m)%m)