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 mCnr(n: Long, r: Long, m: Long): Long {
    val nc = (n - r + 1).until(n + 1).fold(1L) { a, b ->
        (a * (b)) % m
    }
    val rc = 0.until(r).fold(1L) { a, b ->
        (a * (r - b)) % m
    }
    return (nc * mPow(rc, m - 2, m)) % m
}

fun mPow(n: Long, ex: Long, m: Long): Long {
    var x = n
    var remain = ex
    var result = 1L
    while (remain > 0) {
        if (remain % 2L == 1L) {
            result = (result * x) % m
        }
        x = (x * x) % m
        remain /= 2
    }
    return result
}


fun main(args: Array<String>) {
    val m = 1e9.toLong() + 7L
    val (x, y) = readLine()?.split(" ")?.map(String::toInt) ?: return
    if (y > 2 * x || y < x / 2) {
        println("0")
        return
    }
    if ((x + y) % 3 != 0) {
        println("0")
        return
    }
    val c = (x + y) / 3
    val a = (c - Math.abs(y - x)) / 2
    val b = c - a
    val count = mCnr(c.toLong(), Math.max(a, b).toLong(), m)
    
    println(count.toString())
}