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
    }
    println!("{}",if (2*y-x)%3 == 0 && (2*x-y)%3 == 0 { 0 } else { comb((x+y)/3,(2*y-x)/3,1_000_000_007) })
}
 
pub fn comb(n: usize, k: usize, con: usize) -> usize {
    let mut n = n;
    let mut m = 1;
    let mut ret = 1;
    while m <= k  {
        ret = (ret * n * inverse(m,con))%con;
        n -= 1;
        m += 1;
    }
    ret
}

pub fn inverse(n: usize, p:usize) -> usize {
    let mut a = n;
    let mut b = p;
    let mut x1 = 1;
    let mut x2 = 0;
    let mut y1 = 0;
    let mut y2 = 1;
    while b != 0 {
        let r = a%b;
        let q = a/b;
        a = b;
        b = r;
        let temp = x1;
        x1 = x2;
        x2 = temp-q*x2;
        let temp = y1;
        y1 = y2;
        y2 = temp-q*y2;
    }
    x1%p
}
/*
inverse :: Integer -> Integer -> Integer
inverse a b = c `mod` a
    where (_,c,_) = euclid b a

euclid :: Integer -> Integer -> (Integer,Integer,Integer)
euclid a b = euclid' (a,b) (1,0) (0,1) 

euclid' :: (Integer,Integer) -> (Integer,Integer) -> (Integer,Integer) -> (Integer,Integer,Integer)
euclid' (d,0) (x,_) (y,_) = (d,x,y)
euclid' (a,b) (x1,x2) (y1,y2) = euclid' (b,r) (x2,x1-q*x2) (y2,y1-q*y2)
                                   where r = a `mod` b
                                         q = a `div` b
*/