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 Lua (5.3.2) (judge verdict: Accepted)

local mmi, mma = math.min, math.max
local mod = 1000000007
local mfl = math.floor

local function badd(x, y)
  return (x + y) % mod
end
local function bmul(x, y)
  return (x * y) % mod
end

local invs = {1}
local fact = {1}
local invfact = {1}
for i = 2, 500000 do
  fact[i] = bmul(fact[i - 1], i)
  invs[i] = bmul(mfl(mod / i), mod - invs[mod % i])
  invfact[i] = bmul(invfact[i - 1], invs[i])
end

local function getComb(n, k)
  if k == 0 or n == k then return 1 end
  return bmul(fact[n], bmul(invfact[k], invfact[n - k]))
end

local n, k = io.read("*n", "*n")

k = mmi(n - 1, k)
local ret = 0
for i = 0, k do
  local v1 = getComb(n, i)
  local use = n - i
  local v2 = getComb(i + use - 1, use - 1)
  ret = badd(ret, bmul(v1, v2))
end
print(ret)