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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=2e5+10;
const ll p=1e9+7;
int a[N];
ll inv(ll a,ll p) { //p为素数,a<p
    if(a==1)return 1;
    return (p-p/a)*inv(p%a,p)%p;
}
ll C(ll n,ll m){
    ll res=1;
    for(ll i=1,j=n-m+1;i<=m;++i,++j){
        res=res*inv(i,p)%p*j%p;
    }
    return res;
}
int main(){
    ll n,m;
    cin>>n>>m;
    ll res=0;
    ll C1=1,C2=1;
    for(int i=0;i<=min(m,n-1);++i){
        res=(res+C1*C2%p)%p;
        C1=C1*inv(i+1,p)%p*(n-i)%p;
        C2=C2*inv(i+1,p)%p*(n-i-1)%p;
    }
    cout<<res;
    return 0;
}