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 (3.8.2) (judge verdict: Accepted)

#より高速に
def pow(x, n ,p):
    """
    O(log n)
    """
    if n == 0:
        return 1

    K = 1
    while n > 1:
        if n % 2 != 0:
            K = (x*K) % p
        x = (x*x) % p
        n //= 2

    return (K * x) % p




def cmb3(n,r,q):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)    
    s = 1
    for x in range(n,n-r,-1):
        s = (s*x) % q
    t = 1
    for x in range(1,r+1):
        t = (t*x) % q

    #割る数の剰余をどうするかが問題
    u = pow(t,q-2,q)
    return (u * s) % q
  
n,a,b = map(int,input().split())
A = pow(2,n,10**9+7)

if a <= n:
  B = cmb3(n,a,10**9+7)
else:
  B = 0
if b <= n:
  C = cmb3(n,b,10**9+7)
else:
  C = 0

print((A-B-C-1)%(10**9+7))