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)

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;
use std::iter::FromIterator;

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());
    let x = scan.read::<i64>();
    let y = scan.read::<i64>();
    if (2*y - x) % 3 != 0 || (2*x - y) % 3 != 0 {
        println!("{}", 0);
        return;
    }

    let a = (2 * y - x) / 3;
    let b = (2 * x - y) / 3;

    if a < 0 || b < 0 {
        println!("{}", 0);
        return;
    }
    println!("{}", comb(a+b, a));
}

#[allow(dead_code)]
const M: i64 = 1_000_000_007;

// region modulo
#[allow(dead_code)]
use std::ops::*;

#[allow(dead_code)]
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct Co (pub i64);

#[allow(dead_code)]
impl Co {
    pub fn pow(self, mut n: i64) -> Self {
        let mut a = self;
        let mut res = Co(1);
        while n > 0 {
            if n & 1 == 1 {
                res *= a;
            }
            a = a * a;
            n >>= 1;
        }
        res
    }
}

#[allow(dead_code)]
impl std::fmt::Display for Co {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

#[allow(dead_code)]
impl From<i32> for Co {
    fn from(value: i32) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl From<i64> for Co {
    fn from(value: i64) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl From<usize> for Co {
    fn from(value: usize) -> Self {
        Co((value as i64 % M + M) % M)
    }
}
#[allow(dead_code)]
impl AddAssign for Co {
    fn add_assign(&mut self, other: Self) {
        *self = self.add(other);
    }
}
#[allow(dead_code)]
impl Add for Co {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        Co::from((self.0).add(other.0))
    }
}
#[allow(dead_code)]
impl SubAssign for Co {
    fn sub_assign(&mut self, other: Self) {
        *self = self.sub(other);
    }
}
#[allow(dead_code)]
impl Sub for Co {
    type Output = Self;
    fn sub(self, other: Self) -> Self {
        Co::from((self.0).sub(other.0))
    }
}
#[allow(dead_code)]
impl MulAssign for Co {
    fn mul_assign(&mut self, other: Self) {
        *self = self.mul(other);
    }
}
#[allow(dead_code)]
impl Mul for Co {
    type Output = Self;
    fn mul(self, other: Self) -> Self {
        Co::from((self.0).mul(other.0))
    }
}
#[allow(dead_code)]
impl DivAssign for Co {
    fn div_assign(&mut self, other: Self) {
        *self = self.div(other);
    }
}
#[allow(dead_code)]
impl Div for Co {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        self * rhs.pow((M - 2) as i64)
    }
}
// endregion

#[allow(dead_code)]
fn comb(n: i64, r: i64) -> Co {
    let mut ret: Co = Co(1);
    for i in 0..r {
        ret *= (n - i).into();
        ret /= (i + 1).into();
    }
    ret
}

// region template
#[allow(dead_code)]
fn iu(i: i64) -> usize { i as usize }

#[allow(dead_code)]
fn ui(i: usize) -> i64 { i as i64 }

#[allow(dead_code, deprecated)]
fn join<T: std::fmt::Display>(slice: &[T], sep: &str) -> String {
    let strings = slice.iter().map(|t| format!("{}", t)).collect::<Vec<_>>();
    strings.connect(sep)
}

#[allow(dead_code)]
fn arr<'a, S, T>(n: usize, mut f: S) -> Vec<T> where S: FnMut(usize) -> T + 'a {
    (0..n).map(|i| f(i)).collect::<Vec<T>>()
}

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect()
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion