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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		const long MOD = 1000000007;
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			long n = cin.Long();
			long k = cin.Long();

			long m  = Math.Min(k, n - 1);

			ModCounting.InitializeFactorial(n + m);

			ModInt ans = 1;
			for (int i = 1; i <= m; i++) {
				ModInt temp1 = ModCounting.Combination(n, i);
				ModInt temp2 = ModCounting.HomogeneousProduct(n - i, i);
				ans += temp1 * temp2;
			}

			Console.WriteLine(ans.Value);
		}
	}

	public struct ModInt
	{
		public static long Mod { get; set; } = (long)1e9 + 7;

		public static ModInt Pow(ModInt value, long k)
		{
			return Pow(value.Value, k);
		}

		public static ModInt Pow(long value, long k)
		{
			long ret = 1;
			for (k %= Mod - 1; k > 0; k >>= 1, value = value * value % Mod) {
				if ((k & 1) == 1) {
					ret = ret * value % Mod;
				}
			}
			return new ModInt(ret);
		}

		public static ModInt Inverse(ModInt value)
		{
			return Pow(value, Mod - 2);
		}

		public long Value;

		public ModInt(long value)
		{
			value %= Mod;
			if (value < 0) {
				value += Mod;
			}

			Value = value;
		}

		public static ModInt operator +(ModInt lhs, ModInt rhs)
		{
			lhs.Value += rhs.Value;
			if (lhs.Value >= Mod) {
				lhs.Value -= Mod;
			}
			return lhs;
		}

		public static ModInt operator -(ModInt lhs, ModInt rhs)
		{
			lhs.Value -= rhs.Value;
			if (lhs.Value < 0) {
				lhs.Value += Mod;
			}

			return lhs;
		}

		public static ModInt operator *(ModInt lhs, ModInt rhs)
		{
			return new ModInt(lhs.Value * rhs.Value % Mod);
		}
		public static ModInt operator /(ModInt lhs, ModInt rhs)
		{
			long exp = Mod - 2;
			while (exp > 0) {
				if (exp % 2 > 0) {
					lhs *= rhs;
				}

				rhs *= rhs;
				exp /= 2;
			}

			return lhs;
		}

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

			return new ModInt(n);
		}

		public override string ToString()
		{
			return Value.ToString();
		}
	}
	public static class ModCounting
	{
		private static long p_;

		private static long[] factorial_;
		private static long[] inverseFactorial_;
		private static long[] inverse_;

		public static void InitializeFactorial(long max, long p = 1000000007)
		{
			p_ = p;

			factorial_ = new long[max + 1];
			inverseFactorial_ = new long[max + 1];
			inverse_ = new long[max + 1];

			factorial_[0] = factorial_[1] = 1;
			inverseFactorial_[0] = inverseFactorial_[1] = 1;
			inverse_[1] = 1;
			for (int i = 2; i <= max; i++) {
				factorial_[i] = factorial_[i - 1] * i % p;
				inverse_[i] = p - inverse_[p % i] * (p / i) % p;
				inverseFactorial_[i] = inverseFactorial_[i - 1] * inverse_[i] % p;
			}
		}

		public static long Factorial(long n)
		{
			if (n < 0) {
				return 0;
			}

			return factorial_[n];
		}

		public static long InverseFactorial(long n)
		{
			if (n < 0) {
				return 0;
			}

			return inverseFactorial_[n];
		}

		public static long Inverse(long n)
		{
			if (n < 0) {
				return 0;
			}

			return inverse_[n];
		}

		public static long Permutation(long n, long k)
		{
			if (n < k || (n < 0 || k < 0)) {
				return 0;
			}

			return factorial_[n] * inverseFactorial_[n - k] % p_;
		}

		public static long RepeatedPermutation(long n, long k)
		{
			long ret = 1;
			for (k %= p_ - 1; k > 0; k >>= 1, n = n * n % p_) {
				if ((k & 1) == 1) {
					ret = ret * n % p_;
				}
			}

			return ret;
		}

		public static long Combination(long n, long k)
		{
			if (n < k || (n < 0 || k < 0)) {
				return 0;
			}

			return factorial_[n] * (inverseFactorial_[k] * inverseFactorial_[n - k] % p_) % p_;
		}

		public static long HomogeneousProduct(long n, long k)
		{
			if (n < 0 || k < 0) {
				return 0;
			}

			return Combination(n + k - 1, k);
		}
	}


	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}