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: Accepted)

#![allow(
    non_snake_case,
    unused_variables,
    unused_assignments,
    unused_mut,
    dead_code
)]
use proconio::input;
//use proconio::marker::Usize1;
// use proconio::marker::Chars;
//use std::collections::HashSet;
//use std::cmp::*;

const M: i64 = 1000_000_007i64;
fn main() {
    input! {
        x:i64,y:i64
    }
    if (x + y) % 3 != 0 {
        println!("0");
        return;
    }
    let mut ans = 1;
    // 移動回数 = (x+y)/3
    // 一回の移動につき (1,1)の後xまたはy方向に1ずつ進む。
    // したがって、移動Aを x-(x+y)/3 回、 移動Bを y-(x+y)/3回選ぶ、単なるパス選択の並び変えアルゴリズム。
    let x2 = x - (x + y) / 3;
    let y2 = y - (x + y) / 3;
    if x2 < 0 || y2 < 0 {
        println!("0");
        return;
    }
    // ans = (x2+y2)! / (x2! * y2!)
    for i in 1..(x2 + y2) + 1 {
        ans = ans * i % M;
    }
    for i in 1..x2 + 1 {
        ans = ans * modInv(i) % M;
    }
    for i in 1..y2 + 1 {
        ans = ans * modInv(i) % M;
    }
    println!("{}", ans);
}
fn modPow(x: i64, a: i64) -> i64 {
    if a == 1 {
        x
    } else {
        if a % 2 != 0 {
            (modPow(x, a - 1) * x) % M
        } else {
            let t = modPow(x, a / 2);
            t * t % M
        }
    }
}
fn modInv(x: i64) -> i64 {
    modPow(x, M - 2)
}