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)

from scipy.special import comb

n,a,b=map(int,input().split())
m=10**9+7
def mod_m(x):
    return (x+m)%m

def power_a(n,m,a=2):
    ret=1
    while n>0:
        if n%2==1:
            ret=ret*a%m
        a=a*a%m
        n>>=1
    return ret  


def comb_m(a):
    X=1
    Y=1
    for i in range(a):
        X*=(n-i)%m
        Y*=(i+1)%m
    return X*power_a(m-2,m,Y)%m   


varie=mod_m(power_a(n,m)-comb_m(a)-comb_m(b)-1)
          
    
print(int(varie))