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: Runtime Error)

ONE = '1'.freeze
MOD = (10**9) + 7

def inv(x)
  res = 1 # 最終的に x^(MOD-2) になる変数
  beki = x # x^2^n を格納する変数
  # MOD-2の２進数展開を下位のbitから見る
  (MOD - 2).to_s(2).reverse.chars do |digest|
    # bitが立っている <=> digest == ONE 
    # なら resにbekiを掛る
    # ここで、掛け算は計算の都度MODを取る
    res = (beki * res) % MOD if digest == ONE
    # 次のループに備えて、自乗を計算する
    # 計算の都度MODを取る
    beki = (beki * beki) % MOD
  end
  res
end


# 0 となる部屋の組み合わせ * 重複組合せ
n, k = gets.chomp.split(" ").map(&:to_i)
a = 1
ans = 1
k = k >= n ? n - 1 : k

(1..k).each do |i|
   	a *= (N - i) * (N + 1 - i)
    a %= MOD
    a *= inv(i)**2
    a %= MOD
    ans += a
    ans %= MOD
end

puts ans