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 MemoisdCombi
  @fac
  @finv
  @inv
  @modulo

  def initialize(max, mod)
    @modulo = mod
    @fac = Array.new(max)
    @finv = Array.new(max)
    @inv = Array.new(max)

    @fac[0] = @fac[1] = 1
    @finv[0] = @finv[1] = 1
    @inv[1] = 1
    for i in 2..max - 1
      @fac[i] = @fac[i - 1] * i % @modulo
      @inv[i] = @modulo - @inv[@modulo % i] * (@modulo / i) % @modulo
      @finv[i] = @finv[i - 1] * @inv[i] % @modulo
    end
  end

  def combination(n, k)
    return 0 if (n < k)
    return 0 if (n < 0 || k < 0)
    return @fac[n] * (@finv[k] * @finv[n - k] % @modulo) % @modulo
  end
end

# n: 部屋数 (3≤n≤2×10^5)
# k: 移動回数(2≤k≤10^9)

# res: 組み合わせ数
# 重複あり組み合わせ
# n人がn部屋にいるときの組み合わせ総数
modulo = 1000000007
max = 200001

str = gets
n, k = str.chomp.split(" ").map(&:to_i)
ary = Array.new(n)

mc = MemoisdCombi.new(max, modulo)

result = 0
roop_num = [n, k].min

(0..roop_num).each do |m|
  # m: 誰もいない部屋の数
  a = mc.combination(n, m) # nCm
  b = mc.combination(n - 1, m) # n-mHm
  result = (result + (a * b % modulo)) % modulo
end

p result