Problem:
Score : 400 points

Problem Statement

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

1 \leq X \leq 10^6

1 \leq Y \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

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}

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

  val X, Y = in.next().toInt


  val b = ((2.0 / 3) * Y - (1.0 / 3) * X).round.toInt
  val w = ((2.0 / 3) * X - (1.0 / 3) * Y).round.toInt


  val MOD = 1e9.toInt + 7

  if (b >= 0 && w >= 0 && b + 2*w == X && 2*b + w == Y) {
    val mc = new ModComb(w+b, MOD)

    var ans: Long = mc.fact(w+b)
    ans *= mc.factInv(w)
    ans %= MOD
    ans *= mc.factInv(b)
    ans %= MOD

    println(ans)
  }
  else {
    println(0)
  }
}

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
  }

  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()
  }
}