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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import math
n, a, b = map(int, input().split())
mod = 10**9 + 7
ans = 0

f = math.factorial(n)

inv = pow(f, mod - 2, mod)
invs = {}
invs[n] = inv
for m in range(n, 1, -1):
    inv *= m
    inv %= mod
    invs[m - 1] = inv

memo = {}

for i in range(1, n//2+1):
  memo[i] = f*invs[i]*invs[n-i]%mod

for i in range(1, n+1):
  if i != a and i != b:
    if i == n:
      ans += 1
    elif i <= n//2:
      ans += memo[i]
    else:
      ans += memo[n-i]
print(ans%mod)