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: Time Limit Exceeded)

import scala.math._
import scala.util.control.TailCalls._
object Main {
  def solve1(x: Int, y: Int): Int = {
    (x, y) match {
      case (0, 0) =>
        1
      case (x, y) if x < 0 || y < 0 =>
        0
      case _ =>
        val m = solve1(x - 1, y - 2)
        val n = solve1(x - 2, y - 1)
        m + n
    }
  }
  def solve2(x: Int, y: Int): Int = {
    val memo = scala.collection.mutable.Map.empty[(Int, Int), Int]
    def go(x: Int, y: Int): Int = {
      memo.get((x, y)) match {
        case Some(v) =>
          v
        case None =>
          (x, y) match {
            case (0, 0) =>
              memo((0, 0)) = 1; 1
            case (x, y) if x < 0 || y < 0 =>
              0
            case _ =>
              val r = go(x - 1, y - 2) + go(x - 2, y - 1)
              memo((x, y)) = r; r
          }
      }
    }
    go(x, y)
  }

  def solve3(x: Int, y: Int): Int = {
    val memo = scala.collection.mutable.Map.empty[(Int, Int), Int]
    def go(x: Int, y: Int): TailRec[Int] = {
      memo.get((x, y)) match {
        case Some(v) =>
          done(v)
        case None =>
          (x, y) match {
            case (0, 0) =>
              memo((0, 0)) = 1; done(1)
            case (x, y) if x < 0 || y < 0 =>
              done(0)
            case _ =>
              for(m <- tailcall(go(x - 1, y - 2)); n <- tailcall(go(x - 2, y - 1)))
                yield {
                  memo((x, y)) = m + n
                  m + n
                }
          }
      }
    }
    go(x, y).result
  }

  def solve4(x: Int, y: Int, X: Int, Y: Int): Int = {
    val memo = scala.collection.mutable.Map.empty[Int, Int]
    def index(x: Int, y: Int): Int = x + y * (X + 1)
    def go(x: Int, y: Int): TailRec[Int] = {
      val i = index(x, y)
      memo.get(i) match {
        case Some(v) => done(v)
        case None =>
          (x, y) match {
            case (0, 0) =>
              memo(0) = 1; done(1)
            case (x, y) if x < 0 || y < 0 =>
              done(0)
            case _ =>
              for(m <- tailcall(go(x - 1, y - 2)); n <- tailcall(go(x - 2, y - 1)))
                yield {
                  memo(i) = m + n
                  m + n
                }
          }
      }
    }
    go(x, y).result
  }

  def main(args: Array[String]): Unit = {
    val line = Console.in.readLine()
    val Array(tx, ty) = line.split(" ")
    val X = tx.toInt
    val Y = ty.toInt
    val count = solve4(X, Y, X, Y)
    val result = count % (pow(10, 9).toInt + 7)
    print(result)
  }
}