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 Ruby (2.3.3) (judge verdict: Accepted)

class Facts

  def initialize(mod=10**9+7, n_max=1)
    @mod = mod
    @n_max = n_max
    @fact = [1, 1]
    @inv = [0,1]
    @factinv = [1, 1]
    setup_table(n_max) if 1 < @n_max
  end

  def cmb(n,r)
    return 0 if r < 0 || n < r
    setup_table(n) if @n_max < n
    @fact[n] * (@factinv[r] * @factinv[n-r] % @mod) % @mod
  end

  def factorial(n)
    setup_table(n) if @n_max < n
    @fact[n]
  end

  def prm(n,k)
    setup_table(n) if @n_max < n
    @fact[n] * @factinv[n-k] % @mod
  end
  
  def hom(n,k)
    cmb(n+k-1, k)
  end

  private
    # O(t)
    def setup_table(t)
      (@n_max+1).upto(t) do |i|
        @fact.push( @fact[-1] * i % @mod )
        @inv.push( -@inv[@mod % i] * (@mod / i) % @mod )
        @factinv.push( @factinv[-1] * @inv[-1] % @mod )
      end
      @n_max = t
    end
end

mod = 10 ** 9 + 7

n, k = gets.to_s.split.map{|t|t.to_i}

ans = 0
f = Facts.new

[n-1, k].min.downto(0) do |i|
  ans += f.cmb(n, i) * f.hom(n-i, i)
  ans %= mod if ans >= mod
end

puts ans