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 main(args: Array<String>) {
    fun pow(a: Long, b: Long, mod: Int): Long {
        var bt = b
        var ret: Long = 1
        var tmp = a
        while (bt > 0) {
            if (bt and 1 == 1L) ret = ret * tmp % mod
            tmp = tmp * tmp % mod
            bt = bt shr 1
        }
        return ret
    }

    fun nCk(n: Int, k: Int, M: Int): Int {
        var ret: Long = 1
        val min = Math.min(k, n - k)
        for (i in 1..min) {
            ret = ret * pow(i.toLong(), (M - 2).toLong(), M) % M
        }
        for (i in n - min + 1..n) {
            ret = ret * i % M
        }
        return ret.toInt()
    }


    val mod = 1000000007L
    val (x, y) = readLine()!!.split(' ').map(String::toLong)

    val totalMove = (x + y) / 3
    val countU = y - totalMove
    val countR = x - totalMove
    if ((x + y) % 3 != 0L || countU < 0 || countR < 0) {
        println(0)
        return
    }
    println(nCk(totalMove.toInt(), countR.toInt(), mod.toInt()) % mod)
}