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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
namespace mp = boost::multiprecision;
// 任意長整数型
using Bint = mp::cpp_int;
// 仮数部が1024ビットの浮動小数点数型(TLEしたら小さくする)
using Real = mp::number<mp::cpp_dec_float<1024>>;

Bint C(Bint x,Bint y){
  Bint ans=1;
  if(y>x-y){
    y=x-y;
  }
  for(Bint i=0;i<y;i++){
   if((x-i)%2==0&&(x-i)/2<=y){
     ans*=2;
   }
    
   else{
     ans*=(x-i)%1000000007;
   }
    ans%=1000000007;
    
     
  }
 
  return ans;
}


int main(){
  Bint N,a,b,ans=1;
  cin>>N>>a>>b;
  for(Bint i=0;i<N/10;i++){
    ans*=1024;
    ans%=1000000007;
  }
  for(Bint i=0;i<N%10;i++){
    ans*=2;
    ans%=1000000007;
  }
  ans=ans-C(N,a)-C(N,b)-1;
  while(ans<0){
    ans+=1000000007;
  }
  
  cout<<ans;
  cout<<1000000000*999999999;
        
  
}