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: Accepted)

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)

class Combination(maxNum: Int, private val mod: Int) {
    private val fac = LongArray(maxNum + 1).apply { this[0] = 1L; this[1] = 1L }
    private val fInv = LongArray(maxNum + 1).apply { this[0] = 1L; this[1] = 1L }
    private val inv = LongArray(maxNum + 1).apply { this[1] = 1L }

    init {
        for (i in 2..maxNum) {
            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 get(n: Int, k: Int): Long {
        if (n < k) return 0
        if (n < 0 || k < 0) return 0
        return fac[n] * (fInv[k] * fInv[n - k] % mod) % mod
    }
}

fun main(args: Array<String>) {
    val (X, Y) = readIntList()

    if ((X + Y) % 3 != 0) {
        println(0)
        return
    }

    val n = (2 * Y - X) / 3
    val m = (2 * X - Y) / 3

    if (n < 0 || m < 0) {
        println(0)
        return
    }

    val comb = Combination(n+m, 1000000007)
    println(comb.get(n+m, n))
}