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: Runtime Error)

import scala.collection.mutable.ArrayBuffer

object Main extends App {
	val sc = new java.util.Scanner(System.in)
	val pw = new java.io.PrintWriter(System.out)
	
	val x, y = sc.nextLong
	
	lazy val nm = (x+y) / 3L
	
	def cmb(n: Long, k: Long): BigInt = {
		val M = BigInt(1000000007)
		val a = (BigInt(n-k+1) to BigInt(n)).reduce(_ * _ % M)
		(BigInt(2) to BigInt(k)).foldLeft(a)((l, r) => l * r.modInverse(M) % M)
	}
	
	pw.println(if ((x + y) % 3L != 0L || 2*y < x || 2*x < y) BigInt(0) else cmb(nm, x-nm))
	pw.flush()
}