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 Kotlin (1.0.0) (judge verdict: Runtime Error)

fun main(args: Array<String>) {
    val (X, Y) = readLine()!!.split(" ").map { it.toInt() }
    if((2 * X - Y) % 3 != 0 || (2 * Y - X) % 3 != 0){
        println(0)
    }else{
        val x = (2 * X - Y) / 3
        val y = (2 * Y - X) / 3
        if(X >= 0 && y >= 0){
            val c = COM(1000000007, x + y + 1)
            println(c.com(x + y, x))
        }else{
            println(0)
        }
    }
}

class COM(
    val mod: Int,
    val max: Int
) {
    val fac = LongArray(max)
    val finv = LongArray(max)
    val inv = LongArray(max)

    init {
        fac[0] = 1
        fac[1] = 1
        finv[0] = 1
        finv[1] = 1
        inv[1] = 1

        for(i in 2 until max){
            fac[i] = fac[i - 1] * i % mod
            inv[i] = mod - (inv[mod % i] * (mod / i)) % mod
            finv[i] = finv[i - 1] * inv[i] % mod
        }
    }

    fun com(n: Int, k: Int): Long {
        return fac[n] * (finv[k] * finv[n - k] % mod) % mod
    }
}