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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;

fn main() {
    input! {
        x: usize,
        y: usize
    }

    let con = 1_000_000_007;

    let ans = {
        let mut ans = 0;
        for i in (0..=x/2).filter(|i| y == i+2*(x-2*i)) {
            ans += comb(x-i,i);
            ans %= con;
        }
        ans
    };

    println!("{}",ans)
}

pub fn comb(n: usize, k: usize) -> usize {
    let mut n = n;
    let mut k = k;
    let mut ret = 1;
    while k > 0 {
        ret = (ret * n)  / k ;
        n -= 1;
        k -= 1;
    }
    ret
}