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 C (GCC 9.2.1) (judge verdict: Accepted)

typedef long long L;L n,a,b,m=1e9+7;L p(L c,L e){L x=1;for(c%=m;e;e/=2)e&1?x=x*c%m:0,c=c*c%m;return x;}L r(L s,L t){L y=1;for(L i=0;i<t;i++)y=y*(s-i)%m;return y;}main(){scanf("%ld%ld%ld",&n,&a,&b);printf("%ld",(m*m*2+p(2,n)-1-r(n,a)*p(r(a,a),m-2)-r(n,b)*p(r(b,b),m-2))%m);}