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 scala.io.StdIn._
object Main extends App {
  val Array(x, y) = readLine.split(" ").map(_.toInt)
  val Mod = 1000000007
  if (((x + y) % 3 != 0) || (x * 2 < y || y * 2 < x)) {
    println(0)
  } else {
    val n = (x + y) / 3
    val r = x - n
    println(nCr(n, r))
  }

  def nCr(n: Int, r: Int): BigInt = {
    val m = (n - r + 1 to n).foldLeft(1L){(z, l) => z * l % Mod}
    val BIMod = BigInt(Mod)
    (BigInt(2) to BigInt(r)).foldLeft(BigInt(m)){(z, l) => l.modInverse(BIMod) * z % Mod}
  }
}