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) = readIntList()
    val mod = 1000000007
    var list = listOf(Triple(0,0,1))
    if ((2*X - Y)%3 != 0){
        println(0)
        return
    }

    val a = (2*X - Y)/3
    val b = (2*Y - X)/3

    var comb = Comb(a+b, mod)

    val fact = (comb.fac[a+b]*comb.finv[a]%mod)*comb.finv[b]%mod
    println(fact)
}

fun readString() = readLine()!!
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readIntList() = readLine()!!.split(" ").map(String::toInt)
fun readLongList() = readLine()!!.split(" ").map(String::toLong)

fun Int.pow(n:Int) = Math.pow(this.toDouble(), n.toDouble())

class Comb(max:Int, mod:Int) {
    val fac  = LongArray(max+1).apply { this[0] = 1L; this[1] = 1L }
    val finv = LongArray(max+1).apply { this[0] = 1L; this[1] = 1L }
    val inv  = LongArray(max+1).apply { this[1] = 1L }

    init {
        for (i in 2 .. 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
        }
    }
}