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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static Constans;

public static class Constans
{
    public const long Mod = (long)1e9 + 7;
}

public class Combination
{
    private readonly long[] Fact;
    private readonly long[] InvFact;  // モジュラ逆数

    public Combination(long n)
    {
        Fact = new long[n + 1];
        InvFact = new long[n + 1];

        long f = 1;
        Fact[0] = f;
        for (long i = 1; i <= n; i++)
        {
            f *= i;
            f %= Mod;
            Fact[i] = f;
        }

        long inv = ModInt.GetInv(f).Num;

        InvFact[n] = inv;
        for (long i = n - 1; i >= 0; i--)
        {
            InvFact[i] = (InvFact[i + 1] * (i + 1)) % Mod;
        }
    }

    // nCr
    public ModInt GetCombination(long n, long r)
    {
        var comb = Fact[n] * InvFact[r] % Mod;
        comb = comb * InvFact[n - r] % Mod;
        return new ModInt(comb);
    }
}

public struct ModInt
{
    public long Num;

    public ModInt(long num)
    {
        Num = num;
    }

    // x^n
    public static long Power(long x, long n)
    {
        long pow = 1;
        while (n > 0)
        {
            if (n % 2 == 0)
            {
                x *= x;
                x %= Mod;
                n /= 2;
            }
            else
            {
                pow *= x;
                pow %= Mod;
                n--;
            }
        }

        return pow;
    }

    public static ModInt GetInv(long f)
    {
        // フェルマーの小定理 a^(-1) = a^(mod-2)
        return new ModInt(Power(f, Mod - 2));
    }

    public ModInt GetInv()
    {
        return GetInv(Num);
    }

    public override string ToString()
    {
        return Num.ToString();
    }

    public static ModInt operator +(ModInt l, ModInt r)
    {
        l.Num += r.Num;
        if (l.Num >= Mod)
        {
            l.Num -= Mod;
        }
        return l;
    }

    public static ModInt operator -(ModInt l, ModInt r)
    {
        l.Num -= r.Num;
        if (l.Num < 0)
        {
            l.Num += Mod;
        }
        return l;
    }

    public static ModInt operator *(ModInt l, ModInt r)
    {
        return new ModInt(l.Num * r.Num % Mod);
    }

    public static implicit operator ModInt(long n)
    {
        n %= Mod;
        if (n < 0)
        {
            n += Mod;
        }
        return new ModInt(n);
    }
}

public class Solution
{
    public static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        var n = vals[0];
        var k = vals[1];
        var comb = new Combination(n);

        ModInt pattern = 0;
        for (int empty = 0; empty <= Math.Min(k, n - 1); empty++)
        {
            var m = n - empty;
            pattern += comb.GetCombination(n, m) * comb.GetCombination(n - 1, m - 1);
        }
        Console.WriteLine(pattern);
    }
}