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<iostream>
#include<algorithm>
#include<vector>
#include<numeric>
#include<string>
#include<cmath>
#include<set>
#include<queue>
#include<deque>
#include<bitset>
#include<iomanip>
#include<cctype>
#include<map>

#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rep2(i,a,b) for (int (i)=a;(i)<(b);(i)++)
#define all(x) (x).begin(),(x).end()

using namespace std;
const int inf = 1001001000;
const long long int Inf = 1001001001001001000;

void print(vector<vector<int>> a){
	for (int i=0;i<a.size();i++){
		for (int j=0;j<a[i].size();j++){
			cout << a[i][j] << " ";
		}
		cout << endl;
	}
}

void print(vector<vector<long long int>> a){
	for (int i=0;i<a.size();i++){
		for (int j=0;j<a[i].size();j++){
			cout << a[i][j] << " ";
		}
		cout << endl;
	}
}

void print(vector<int> a){
    int n = a.size();
    for (int j=0;j<n;j++) {
        if (j != n-1) cout << a[j] << " ";
        else cout << a[j] << endl;
    }
}

//mod計算用のクラス
class ModInt{
public:
    long long int x;
    long long int mod;
	ModInt(){}
    ModInt(long long int _x, long long int _mod = 1000000007){
        this->x = _x % _mod;
        this->mod = _mod;
    }
	ModInt operator+(ModInt other){
		return ModInt(this->x + (other.x % this->mod),this->mod);
	}
	ModInt operator-(ModInt other){
		long long int res = this->x - (other.x % this->mod);
		if (res < 0) return ModInt(res + this->mod, this->mod);
		return ModInt(res);
	}
	ModInt operator*(ModInt other){
		return ModInt(this->x * (other.x % this->mod),this->mod);
	}
	ModInt operator/(ModInt other){
		return ModInt(*this * other.inv());
	}
	ModInt pow(long long int n){
		ModInt res(1, this->mod), a(this->x, this->mod);
		while (n){
			if (n & 1){
				res = res * a;
			}
			n >>= 1;
			a = a * a;
		}
		return res;
	}
	ModInt inv(){
		return ModInt(this->pow(this->mod - 2));
	}
	void disp(){
		cout << this->x << endl;
	}
};
ostream& operator<<(ostream& stream, const ModInt m){
	stream << to_string(m.x);
	return stream;
}

class modcomb{
	public:
		vector<ModInt> fact;
		vector<ModInt> ifact;
		modcomb(){}
		modcomb(int n){
			this->fact.resize(n + 1, ModInt(1));
			this->ifact.resize(n + 1, ModInt(1));
			for (int i = 1; i <= n;i++)
				this->fact[i] = this->fact[i - 1] * i;
			this->ifact[n] = fact[n].inv();
			for (int i = n; i >= 1; --i)
				this->ifact[i - 1] = ifact[i] * i;
		}
		ModInt operator()(int n, int k){
			if (k < 0 || k > n)
				return 0;
			return this->fact[n] * this->ifact[k] * this->ifact[n - k];
		}
};

int main()
{
	int n, k;
	cin >> n >> k;
	k = min(k, n - 1);
	modcomb c(n);
	ModInt ans(0);
	rep(i, k+1)
	{
		ans = ans + c(n,i)*c((n-i-1)+i, i);
	}
	cout << ans << endl;

	return 0;
}