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 (1.15.1) (judge verdict: Accepted)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]

#[allow(unused_macros)]
macro_rules! invec {
    ( $ t : ty ) => {{
        let mut s = String::new();
        match std::io::stdin().read_line(&mut s) {
            Ok(0) => Vec::<$t>::new(),
            Ok(n) => s
                .trim()
                .split_whitespace()
                .map(|s| s.parse::<$t>().unwrap())
                .collect::<Vec<$t>>(),
            Err(_) => Vec::<$t>::new(),
        }
    }};
}

#[allow(unused_macros)]
macro_rules! get {
      ($t:ty) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.trim().parse::<$t>().unwrap()
          }
      };
      ($($t:ty),*) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              let mut iter = line.split_whitespace();
              (
                  $(iter.next().unwrap().parse::<$t>().unwrap(),)*
              )
          }
      };
      ($t:ty; $n:expr) => {
          (0..$n).map(|_|
              get!($t)
          ).collect::<Vec<_>>()
      };
      ($($t:ty),*; $n:expr) => {
          (0..$n).map(|_|
              get!($($t),*)
          ).collect::<Vec<_>>()
      };
      ($t:ty ;;) => {
          {
              let mut line: String = String::new();
              std::io::stdin().read_line(&mut line).unwrap();
              line.split_whitespace()
                  .map(|t| t.parse::<$t>().unwrap())
                  .collect::<Vec<_>>()
          }
      };
      ($t:ty ;; $n:expr) => {
          (0..$n).map(|_| get!($t ;;)).collect::<Vec<_>>()
      };
}

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

macro_rules! echo {
    ($($a:expr),*) => {
          $(println!("{}",$a))*
      }
}

struct SliceDisplay<'a, T: 'a>(&'a [T]);
impl<'a, T: std::fmt::Display + 'a> std::fmt::Display for SliceDisplay<'a, T> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        for item in self.0 {
            write!(f, "{} ", item)?;
        }
        Ok(())
    }
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;
#[allow(dead_code)]
static M_O_D: usize = 1000000007;
static PAI: f64 = 3.1415926535897932;

#[derive(Debug, Copy, Clone)]
pub struct ModInt {
    x: i64,
    global_mod: i64,
}
impl ModInt {
    pub fn new(p: i64) -> Self {
        let gm = 1000000007;
        let a = (p % gm + gm) % gm;
        return ModInt {
            x: a,
            global_mod: gm,
        };
    }
    pub fn inv(self) -> Self {
        return self.pow(self.global_mod - 2);
    }
    pub fn pow(self, t: i64) -> Self {
        if (t == 0) {
            return ModInt::new(1);
        };
        let mut a = self.pow(t >> 1);
        a = a * a;
        if (t & 1 != 0) {
            a = a * self
        };
        return a;
    }
}
impl Add for ModInt {
    type Output = ModInt;
    fn add(self, other: ModInt) -> ModInt {
        let ret = self.x + other.x;
        return ModInt::new(ret);
    }
}
impl Sub for ModInt {
    type Output = ModInt;
    fn sub(self, other: ModInt) -> ModInt {
        let ret = self.x - other.x;
        return ModInt::new(ret);
    }
}
impl Mul for ModInt {
    type Output = ModInt;
    fn mul(self, other: ModInt) -> ModInt {
        let ret = self.x * other.x;
        return ModInt::new(ret);
    }
}
impl Div for ModInt {
    type Output = ModInt;
    fn div(self, other: ModInt) -> ModInt {
        let ret = self.x * other.inv().x;
        return ModInt::new(ret);
    }
}
impl std::string::ToString for ModInt {
    fn to_string(&self) -> String {
        return self.x.to_string();
    }
}
pub struct Combination {
    fact: Vec<ModInt>,
    ifact: Vec<ModInt>,
}
impl Combination {
    pub fn new(n: i32) -> Self {
        let mut fact = vec![ModInt::new(0); (n + 1) as usize];
        let mut ifact = vec![ModInt::new(0); (n + 1) as usize];
        fact[0] = ModInt::new(1);
        for i in 1..n + 1 {
            fact[i as usize] = fact[(i - 1) as usize] * ModInt::new(i as i64)
        }
        ifact[n as usize] = fact[n as usize].inv();
        for i in (1..n + 1).rev() {
            ifact[(i - 1) as usize] = ifact[i as usize] * ModInt::new(i as i64)
        }
        let a = Combination {
            fact: fact,
            ifact: ifact,
        };
        return a;
    }
    #[macro_use]
    pub fn gen(self, n: i32, k: i32) -> ModInt {
        mydbg!(self.fact[n as usize]);
        mydbg!(self.ifact[k as usize]);
        mydbg!(self.ifact[(n - k) as usize]);
        if (k < 0 || k > n) {
            return ModInt::new(0 as i64);
        };
        return self.fact[n as usize] * self.ifact[k as usize] * self.ifact[(n - k) as usize];
    }
}
fn main() {
    input! {
       mut x:usize,
       mut y:usize,
    }

    if (x + y) % 3 != 0 {
        echo!(0);
        return;
    }
    let m = (x + y) / 3;

    let a = 2 * m - y;
    mydbg!(m, a);
    let mut c = Combination::new(m as i32);
    let ans = c.gen((a + (m - a)) as i32, a as i32);
    echo!(ans.x);
}