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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
var input=require("fs").readFileSync("/dev/stdin","utf8");
var cin=input.split(/ |\n/),cid=0;
function next(a){return a?cin[cid++]:+cin[cid++];}
function nexts(n,a){return a?cin.slice(cid,cid+=n):cin.slice(cid,cid+=n).map(a=>+a);}
function nextm(h,w,a){var r=[],i=0;if(a)for(;i<h;i++)r.push(cin.slice(cid,cid+=w));else for(;i<h;i++)r.push(cin.slice(cid,cid+=w).map(a=>+a));return r;}
function xArray(v){var a=arguments,l=a.length,r="Array(a["+--l+"]).fill().map(x=>{return "+v+";})";while(--l)r="Array(a["+l+"]).fill().map(x=>"+r+")";return eval(r);}

var mod = 1e9+7;
function mul(){for(var a=arguments,r=a[0],i=a.length;--i;)r=((r>>16)*a[i]%mod*65536+(r&65535)*a[i])%mod;return r;}
var fac=[],finv=[],invs=[],pow2=[];
function fset(n){
  fac.length=n+1,fac[0]=fac[1]=1;
  for(var i=2;i<=n;)fac[i]=mul(fac[i-1],i++);
  finv.length=n+1,finv[0]=finv[1]=1,finv[n]=inv(fac[n]);
  for(i=n;2<i;)finv[i-1]=mul(finv[i],i--);
  invs.length=n+1,invs[0]=invs[1]=1;
  for(i=2;i<=n;)invs[i]=mul(fac[i-1],finv[i++]);
  pow2.length=n+1,pow2[0]=1;
  for(i=1;i<=n;i++)pow2[i]=pow2[i-1]*2%mod;
}
function inv(b){for(var a=mod,u=0,v=1,t;b;v=t)t=a/b|0,a-=t*b,u-=t*v,t=a,a=b,b=t,t=u,u=v;u%=mod;return u<0?u+mod:u;}
function pow(a,n){for(var r=1;n;a=mul(a,a),n>>=1)if(n&1)r=mul(a,r);return r;}
function ncr(n,r){return mul(fac[n],finv[r],finv[n-r]);}
function npr(n,r){return mul(fac[n],finv[r]);}

var myOut = main();
if(myOut !== undefined)console.log(myOut);

function main(){
  var n = next(), a = next(), b = next();
  var ans = pow(2,n) - 1, x = 1;
  for(var i = 1; i <= b; i++){
    x = mul(x,n-i+1,inv(i));
    if(i === a)ans -= x;
  }
  ans -= x;
  ans %= mod;
  ans += mod;
  return ans %= mod;
}