Problem:
Score : 500 points

Problem Statement

There is a building with n rooms, numbered 1 to n.

We can move from any room to any other room in the building.

Let us call the following event a move: a person in some room i goes to another room j~ (i \neq j).

Initially, there was one person in each room in the building.

After that, we know that there were exactly k moves happened up to now.

We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?

Find the count modulo (10^9 + 7).

Constraints

All values in input are integers.

3 \leq n \leq 2 \times 10^5

2 \leq k \leq 10^9

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).

Sample Input 1

3 2

Sample Output 1

10

Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

(0, 0, 3)

(0, 1, 2)

(0, 2, 1)

(0, 3, 0)

(1, 0, 2)

(1, 1, 1)

(1, 2, 0)

(2, 0, 1)

(2, 1, 0)

(3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000

Sample Output 2

607923868

Print the count modulo (10^9 + 7).

Sample Input 3

15 6

Sample Output 3

22583772

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(), k = next();
  fset(2*n);
  var ans = ncr(n+n-1,n);
  for(var i = k+1; i < n; i++){
    var t = n - i;
    ans -= mul(ncr(n-1,t-1),ncr(n,i));
  }
  ans %= mod;
  ans += mod;
  return ans % mod;
}