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 5.4.1) (judge verdict: Accepted)

    #include<stdio.h>
    #define MOD 1000000007
    #define ll long long
    ll modpow(ll a,ll n,ll mod){
        ll result=1;
        while(n>0){
            if(n&1)
                result=result*a%mod;
            a=a*a%mod;
            n/=2;
        }
        return result;
    }
    ll modinv(ll a,ll mod){
        return modpow(a,mod-2,mod);
    }
    int main(){
        int n,a,b,i;
        ll ans=0,m=1,c;
        scanf("%d%d%d",&n,&a,&b);
        ans=(modpow(2,n,MOD)-1)%MOD;
        c=n;
        for(i=2;i<=a;i++){
            m=m*i%MOD;
            c=c*(n-i+1)%MOD;
        }
        ans=(ans-c*modinv(m,MOD))%MOD;
        for(;i<=b;i++){
            m=m*i%MOD;
            c=c*(n-i+1)%MOD;
        }
        ans=(ans-c*modinv(m,MOD))%MOD;
        while(ans<0){
            ans+=MOD;
        }
        printf("%lld\n",ans);
        return 0;
    }