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 Ruby (2.3.3) (judge verdict: Runtime Error)


n,a,b = gets.chop.split.map(&:to_i)
sum = 0

def combi(n,k)
  k=n-k if 2*k > n
  return 1 if k == 0
  ((n-k+1)..n).reduce(&:*)/((1..k).reduce(&:*))
end

memo = {}

pascal = ->(n) {
  each_cons = ->(ar) {
    (ar.size < 2) ? [] : [ar[0] + ar[1]] + each_cons[ar.drop(1)]
  }
  return memo[n] if memo.has_key?(n)
  memo[n] = n.zero? ? [1] : [1] + each_cons[pascal[n - 1]] + [1]
}

#n = 8
#2.times {|i| puts pascal[i].join(" ").center(30)}

print(((pascal[n].inject(:+)-1-combi(n,a)-combi(n,b))%(10**9+7)))