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)

#define _USE_MATH_DEFINES
#include <cstdio>
#include <iostream>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <complex>
#include <string>
#include <vector>
#include <array>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <limits>
#include <climits>
#include <cfloat>
#include <functional>
#include <iterator>
#include <memory>
#include <regex>
using namespace std;

void mod_inverse(int n, vector<long long>& inv, int mod)
{
    inv.assign(n+1, -1);
    inv[1] = 1;
    for(int i=2; i<=n; ++i)
        inv[i] = inv[mod % i] * (mod - mod / i) % mod;
}

class FactorialCalculation
{
private:
    const int mod;
    vector<long long> factorial;
    vector<long long> invFactorial;
public:
    FactorialCalculation(int n, int mod) : mod(mod)
    {
        factorial.resize(n+1, 1);
        invFactorial.resize(n+1, 1);
        vector<long long> inv;
        mod_inverse(n, inv, mod);
        for(int i=1; i<=n; ++i){
            factorial[i] = factorial[i-1] * i % mod;
            invFactorial[i] = invFactorial[i-1] * inv[i] % mod;
        }
    }
    long long getFactorial(int n){
        return factorial[n];
    }
    long long getInvFactorial(int n){
        return invFactorial[n];
    }
    long long getPermutation(int n, int r){
        if(n < r)
            return 0;
        return factorial[n] * invFactorial[n-r] % mod;
    }
    long long getCombination(int n, int r){
        if(n < r)
            return 0;
        return getPermutation(n, r) * invFactorial[r] % mod;
    }
    long long getHomogeneous(int n, int r){
        if(n == 0 && r == 0)
            return 1;
        return getCombination(n+r-1, r);
    }
};

const int MOD = 1000000007;

int main()
{
    int n, k;
    cin >> n >> k;
    FactorialCalculation fc(n*2, MOD);

    long long ans = 0;
    for(int i=0; i<=min(n-1,k); ++i){
        long long tmp = fc.getCombination(n, i);
        tmp *= fc.getHomogeneous(n-i, i);
        tmp %= MOD;
        ans += tmp;
        ans %= MOD;
    }
    cout << ans << endl;

    return 0;
}