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 OCaml (4.02.3) (judge verdict: Accepted)

let m = 1000000007
let ( +^ ) x y = (x + y) mod m
let ( -^ ) x y = x +^ (m - y)
let ( *^ ) x y = (x * y) mod m

let rec power ( * ) e m n =
  if n <= 0 then e
  else power ( * ) (if n land 1 = 0 then e else m * e) (m * m) (n lsr 1)

let perm n k =
  Array.fold_left ( *^ ) 1 @@
  Array.init k @@ fun i -> (i + n - k + 1) mod m
let comb n k = power ( *^ ) (perm n k) (perm k k) (m - 2)

let () = Scanf.scanf "%d %d" @@ fun n k ->
  let perm_n = Array.make (min n k + 1) 1 in
  let perm_n1 = Array.make (min n k + 1) 1 in
  let perm_kk = Array.make (min n k + 1) 1 in
  for i = 0 to min n k - 1 do
    perm_n.(i + 1) <- (n - i) mod m *^ perm_n.(i);
    perm_n1.(i + 1) <- (n - i - 1) mod m *^ perm_n1.(i);
    perm_kk.(i + 1) <- (i + 1) *^ perm_kk.(i)
  done;
  let combn k = power ( *^ ) perm_n.(k) perm_kk.(k) (m - 2) in
  let combn1 k = power ( *^ ) perm_n1.(k) perm_kk.(k) (m - 2) in
  Printf.printf "%d\n" @@
  Array.fold_left ( +^ ) 0 @@
  Array.init (min n k + 1) @@ fun i -> combn i *^ combn1 i