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: Runtime Error)

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

namespace test
{
    class MainClass
    {
        /*
        public static int Digit(int num)
        {
            return (num == 0) ? 1 : ((int)Math.Log10(num) + 1);
        }

        public static int Sum_n(int num)
        {
            int digit = Digit(num);
            int p = 0;
            
            for (int i = digit; i>0; i--)
            {
                int temp = num % 10;
                p += temp;
                num = num / 10;
            }
            return p;
        }
        public static class Combination
        {
            public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition){
                if(k == 1)
                {
                    foreach (var item in items)
                        yield return new T[] { item };
                    yield break;
                }
                foreach (var item in items)
                {
                    var leftside = new T[] { item };

                    var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                    foreach(var rightside in Enumerate(unused, k-1, withRepetition))
                    {
                        yield return leftside.Concat(rightside).ToArray();
                    }
                }
            } 
        }
        */

        public static long Factorial(int n) =>
            n == 0 ? 1L : n * Factorial(n - 1);

        public static void Main(string[] args)
        { 
            string[] str = Console.ReadLine().Split(' ');
            
            int d = (int)Math.Pow(10, 9) + 7;
            int n = int.Parse(str[0]);
            int k = int.Parse(str[1]);
            long ans = 0;
            int Ans = 0;
            for (int i = 0; i < n; i++) {
                long C = Factorial(n) / (Factorial(n - i)*Factorial(i));
                long H = Factorial(n - 1) / (Factorial(i) * Factorial(n - i - 1));
                ans += C * H;
            }
            ans = ans % d;
            Ans = (int)ans;

            Console.WriteLine(Ans);
            
            


        }

    }

}