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 Scala (2.11.7) (judge verdict: Accepted)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Stack, Queue, PriorityQueue, Set}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val MOD = 1e9.toInt + 7

  val n, k = in.next().toInt

  val mc = new ModComb(n, MOD)
  var ans = 0L

  for (i <- 1 to (k min (n-1))) {

    val ball = i
    val stick = (n-i)-1
    ans += mc.comb(n, i) * mc.comb(ball+stick, stick)
    ans %= MOD
  }

  if (k % 2 == 0 || k >= 3) {
    ans += 1
  }

  println(ans)
}


class ModComb(maxNum: Int, mod: Long) {

  private def repeatSquares(x: Long, n: Long): Long = {
    if(n == 0)
      1
    else if(n % 2 == 0)
      repeatSquares(x*x % mod, n/2)
    else
      (x * repeatSquares(x*x % mod, n/2)) % mod
  }

  private val fact = new Array[Long](maxNum + 1)

  fact(0) = 1
  for (i <- 1 to maxNum)
    fact(i) = (i * fact(i-1)) % mod

  val factInv = new Array[Long](maxNum + 1)

  factInv(maxNum) = repeatSquares(fact(maxNum), mod-2)
  for (i <- (1 to maxNum).reverse)
    factInv(i-1) = (i * factInv(i)) % mod


  // nCk
  def comb(n: Int, k: Int): Long = {
    val numer = fact(n)
    val denom = (factInv(n-k) * factInv(k)) % mod

    (numer * denom) % mod
  }

}


object Sub {
  def print2DimArray[A](mat: Array[Array[A]]): Unit = {
    mat.foreach(lin => println(lin.deep))
  }
}

class InputReader(stream: InputStream) {
  private[this] val reader = new BufferedReader(new InputStreamReader(stream))
  private[this] var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}