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 (1.3.71) (judge verdict: Accepted)

fun main(args: Array<String>) {
    var (x, y) = readIntList()

    if ((x + y) % 3 != 0) {
        println(0)
        return
    }
    val n = (x + y) / 3
    x -= n
    y -= n
    if (x < 0 || y < 0) {
        println(0)
        return
    }
    val mod = 1_000_000_007L
    val comb = CombinationModPrime(x + y, mod)
    println(comb.operate(x + y, x))
}

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

fun Long.modPow(t: Long, mod: Long): Long {
    if (t == 0L) return 1L
    var a = this.modPow(t shr 1, mod)
    a *= a
    a %= mod
    if (t and 1 == 1L) {
        a *= this
        a %= mod
    }
    return a
}

// mod pの逆元 (pは素数)
fun Long.modInverse(mod: Long) = this.modPow(mod - 2L, mod)

class CombinationModPrime(private val n: Int, private val mod: Long) {
    private val fact = Array(n + 1) { 0L }
    private val ifact = Array(n + 1) { 0L }

    init {
        fact[0] = 1
        for (i in 1..n) {
            val tmp = fact[i - 1] * i.toLong()
            fact[i] = tmp % mod
        }
        ifact[n] = fact[n].modInverse(mod)
        for (i in n downTo 1) {
            val tmp = ifact[i].toLong() * i.toLong()
            ifact[i - 1] = tmp % mod
        }
    }

    fun operate(n: Int, k: Int): Int {
        if (k < 0 || k > n) return 0
        var tmp = fact[n] * ifact[k]
        tmp %= mod
        tmp *= ifact[n - k]
        tmp %= mod
        return tmp.toInt()
    }
}