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 (2.4.0) (judge verdict: Accepted)

n,a,b=map(int,input().split())
MOD=10**9+7
def inv(a):
  return pow(a,MOD-2,MOD)

def choose(n,r):
  if r==0 or r==n:
    return 1
  else:
    A=B=1
    ls_A=[1]
    ls_B=[1]
    for i in range(r):
      A=ls_A[i]*(n-i)%MOD
      ls_A.append(A)
      B=ls_B[i]*(i+1)%MOD
      ls_B.append(B)
    return ls_A[r]*inv(ls_B[r])%MOD

def pow_k(x,n):
    if n==0:
        return 1
    K=1
    while n>1:
        if n%2 != 0:
            K=K*x%MOD
            x=x**2%MOD
            n=(n-1)//2
        else:
            x=x**2%MOD
            n=n//2%MOD
    return K*x%MOD 

print((pow_k(2,n)-1-choose(n,a)-choose(n,b))%MOD)