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 ModCombination
  attr_reader :fac, :inv, :finv, :mod

  MOD = 10 ** 9 + 7

  def initialize(n, mod: MOD)
    @mod = mod
    @fac = [1, 1]
    @inv = [1, 1]
    @finv = [1, 1]

    (2..n).each do |i|
      @fac[i] = fac[i - 1] * i % mod
      @inv[i] = mod - inv[mod % i] * (mod / i) % mod
      @finv[i] = finv[i - 1] * inv[i] % mod
    end
  end

  def combination(n, k)
    return 0 if n < k
    return 0 if n < 0 || k < 0

    fac[n] * (finv[k] * finv[n - k] % mod) % mod
  end

  def repeated_combination(n, k)
    combination(n + k - 1, k)
  end
end

MOD = 10 ** 9 + 7
N, K = gets.split.map(&:to_i)
mc = ModCombination.new(2 * N + 1)
ans = 0

0.upto([K, N - 1].min) do |m|
  ans += mc.combination(N, m) * mc.repeated_combination(N - m, m)
  ans %= MOD
end

puts ans