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.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.nextInt
	
	val M = BigInt(1000000007)
	val nm = (x+y) / 3
	
	def cmb(n: Int, k: Int): BigInt =
		(BigInt(1) to BigInt(k)).foldLeft(BigInt(1))((z, i) => (n - k + i) * i.modInverse(M) * z % M)
	
	pw.println(if (((x+y) % 3 != 0) || (2*y < x || 2*x < y)) 0 else cmb(nm, x - nm).toInt)
	pw.flush()
}