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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

public class Program
{
    static List<Mint> F;
    public static void Main(string[] args)
    {
        var input = Console.ReadLine().Split().Select(int.Parse).ToList();
        var n = input[0];
        var k = input[1];
        if (k >= n - 1)
        {
            Console.WriteLine(Mint.Combination(n * 2 - 1, n));
        }
        else
        {
            F = new [] { new Mint(1) }.ToList();
            foreach (var i in Enumerable.Range(1, n))
            {
                F.Add(F.Last() * i);
            }
            Console.WriteLine(Func(n, k));
        }
    }

    static Mint Func(int n, int k)
    {
        return k == 0 ? new Mint(1) : Comb(n - 1, k) * Comb(n, k) + Func(n, k - 1);
    }

    static Mint Comb(int n, int k) => F[n] / F[k] / F[n - k];
}

public class Mint
{
    public const long Mod = (long)1e9 + 7;
    public long Number { get; private set; }
    public Mint Inv => Pow(Mod - 2);

    public Mint(long number = 0)
    {
        Number = (number % Mod + Mod) % Mod;
    }

    public Mint Pow(long t)
    {
        if (t == 0)
        {
            return new Mint(1);
        }

        var result = Pow(t >> 1);
        result *= result;

        if ((t & 1) > 0)
        {
            result *= this;
        }

        return result;
    }

    public static Mint Combination(Mint m, Mint n)
        => Permutation(m, n) / Permutation(n, n);

    public static Mint Permutation(Mint m, Mint n)
        => n.Number == 0 ? new Mint(1) : Enumerable.Range(m - n + 1, n).Select(target => new Mint(target)).Aggregate((a, b) => a * b);

    public static Mint operator +(Mint m) => m;
    public static Mint operator -(Mint m) => new Mint(-m.Number);
    public static Mint operator +(Mint a, Mint b) => new Mint(a.Number + b.Number);
    public static Mint operator -(Mint a, Mint b) => new Mint(a.Number - b.Number);
    public static Mint operator *(Mint a, Mint b) => new Mint(a.Number * b.Number);
    public static Mint operator /(Mint a, Mint b) => a * b.Inv;
    public static implicit operator Mint(long i) => new Mint(i);
    public static implicit operator Mint(int i) => new Mint(i);
    public static implicit operator long(Mint m) => m.Number;
    public static implicit operator int(Mint m) => (int)m.Number;
    public override string ToString() => Number.ToString();
}