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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun expt-10-9 (base n)
  (let* ((arr (make-array 100 :element-type 'fixnum :initial-element 0))
         (a (format nil "~b" n)))
    (labels ((expt-f (k)
               (if (= k 1)
                   base
                   (setf (aref arr (floor (log k 2)))
                         (mod (expt (expt-f (/ k 2)) 2) 1000000007))))
             (10-9-* (x y) (mod (* x y) 1000000007)))
    (setf (aref arr 0) base)
    (expt-f (expt 2 (1+ (length a))))
    (mod (reduce #'10-9-* (map 'list (lambda (x y) (if (char= x #\0) 1 y)) (reverse a) arr)) 1000000007))))

(defun !-10-9 (n a ans)
  (if (= n (1- a))
      ans
      (!-10-9 (1- n) a (mod (* n ans) 1000000007))))

(defun c (n a)
  (* (!-10-9 n (- n a -1) 1) (expt-10-9 (!-10-9 a 1 1) 1000000005)))

(let* ((n (read))
       (a (read))
       (b (read)))
  (princ (mod (- (expt-10-9 2 n) 1 (c n a) (c n b)) 1000000007)))