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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

base :: Integer
base = 1000000007

times :: Integer -> Integer -> Integer
times a b = a * b `mod` base

minus :: Integer -> Integer -> Integer
minus a b
   | a < b     = a-b + base
   | otherwise = a-b

power :: Integer -> Integer -> Integer
power n k
   | k == 0         = 1
   | k `mod` 2 == 0 = power (times n n) (k`div`2)
   | otherwise      = times n $! power n (k-1)

inv :: Integer -> Integer
inv n = power n $ base - 2

allPatterns :: Integer -> Integer
allPatterns n = power 2 n - 1

binom :: Integer -> Integer -> Integer
binom n m
   | (n-m) < m = times (foldr times 1 [m+1..n]) $ inv $ foldr times 1 [1..n-m]
   | otherwise = times (foldr times 1 [n-m+1..n]) $ inv $ foldr times 1 [1..m]

main = do
   [n,a,b] <- map (read :: String -> Integer) . words <$> getLine
   putStrLn $ show $ minus (allPatterns n) $ (binom n a) + (binom n b) `mod` base