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)

Scanf.scanf "%d %d" (fun n k ->
    let m = 1_000_000_007 in

    let extgcd x y =
        let rec eg r0 r1 a0 a1 b0 b1 =
            if r1 = 0 then a0, b0 else
                let q1 = r0 / r1 in
                eg r1 (r0 mod r1) a1 (a0 - q1 * a1) b1 (b0 - q1 * b1)
        in
        eg x y 1 0 0 1
    in

    let inv x y = (* 1/x in mod y *)
        let c, d = extgcd x y in
        if c < 0 then c + y else c
    in
    let ( +@) a b = (a + b) mod m in
    let ( -@) a b = (((a - b) mod m) + m) mod m in
    let ( *@) a b = ((a mod m) * (b mod m)) mod m in
    let ( /@) a b = a *@ inv b m in
    let rec loop i r1 r2 a b acc =
        if i > n || i > k then acc else (
            let acc = acc +@ r1 *@ r2 in
            let r1 = r1 *@ a /@ b in
            let r2 = r2 *@ (a - 1) /@ b in
            let a = a - 1 in
            let b = b + 1 in
            loop (i + 1) r1 r2 a b acc
        )
    in
    loop 0 1 1 n 1 0 |> Printf.printf "%d\n"
)