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: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            var NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = NK[0];
            var K = NK[1];

            //0が0個の時
            var ans = new Modular(1);

            //0がi個の時
            for (long i = 1; i <= K && i < N; i++)
            {
                ans += Modular.Ncr((int)N, (int)i) * Modular.Ncr((int)(N-1), (int)i-1);
            }
            Console.WriteLine(ans.value% 1000000007); 
        }

    }

    class Modular
    {
        private const int M = 1000000007;
        public long value;
        public Modular(long value) { this.value = value; }
        public static implicit operator Modular(long a)
        {
            var m = a % M;
            return new Modular((m < 0) ? m + M : m);
        }
        public static Modular operator +(Modular a, Modular b)
        {
            return (a.value + b.value) % M;
        }
        public static Modular operator -(Modular a, Modular b)
        {
            return a.value - b.value;
        }
        public static Modular operator *(Modular a, Modular b)
        {
            return a.value * b.value;
        }
        public static Modular Pow(Modular a, int n)
        {
            switch (n)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular operator /(Modular a, Modular b)
        {
            return a * Pow(b, M - 2);
        }
        private static readonly List<int> facs = new List<int> { 1 };
        private static Modular Fac(int n)
        {
            for (int i = facs.Count; i <= n; ++i)
            {
                facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
            }
            return facs[n];
        }
        public static Modular Ncr(int n, int r)
        {
            return (n < r) ? 0
                 : (n == r) ? 1
                            : Fac(n) / (Fac(r) * Fac(n - r));
        }
        public static explicit operator int(Modular a)
        {
            return (int)a.value;
        }

        public static Modular Lcm(Modular a, Modular b)
        {
            var tmp = Gcdl(a.value, b.value);
            return ((a * b) / new Modular(tmp));
        }
        static Modular Gcd(Modular m, Modular n)
        {
            if (n.value > m.value) return Gcd(n, m);
            if (n.value == 0) return m;
            var r = new Modular(m.value % n.value);
            return Gcd(n, r);
        }

        static long Gcdl(long m, long n)
        {
            if (n > m) return Gcdl(n, m);
            if (n == 0) return m;
            return Gcdl(n, m % n);
        }
    }
}