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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use self::mod_combin::ModCombin;
use proconio::input;

fn main() {
    input! {
        x: usize,
        y: usize,
    };
    if (x + y) % 3 != 0 {
        println!("{}", 0);
        return;
    }
    let n = (x + y) / 3;
    let (x1, y1) = (x - n, y - n);
    let mc = ModCombin::new(x1 + y1);
    let ans = mc.combination(x1 + y1, x1);
    println!("{}", ans);
}

mod mod_u32 {
    #[derive(Clone, Copy, Debug, Eq, PartialEq)]
    pub struct ModU32(u32);

    const MODP: u32 = 1_000_000_007;

    impl ModU32 {
        pub fn inv(self) -> Self {
            if self.0 == 0 {
                panic!()
            };
            self.pow(MODP - 2)
        }

        pub fn new(x: u64) -> Self {
            Self((x % (MODP as u64)) as u32)
        }

        pub fn pow(self, exp: u32) -> Self {
            let mut b: ModU32 = self;
            let mut a: ModU32 = Self::new(1);
            let mut x = exp;
            while x > 1 {
                if x & 1 == 1 {
                    a *= b;
                }
                x /= 2;
                b *= b;
            }
            if x == 1 {
                a *= b;
            }
            a
        }
    }

    impl From<i32> for ModU32 {
        fn from(x: i32) -> Self {
            ModU32::from(x as i64)
        }
    }

    impl From<i64> for ModU32 {
        fn from(x: i64) -> Self {
            let n = x % (MODP as i64);
            ModU32::new(if n.is_negative() { MODP as i64 + n } else { n } as u64)
        }
    }

    impl From<u32> for ModU32 {
        fn from(x: u32) -> Self {
            ModU32::from(x as u64)
        }
    }

    impl From<u64> for ModU32 {
        fn from(x: u64) -> Self {
            ModU32::new(x)
        }
    }

    impl From<usize> for ModU32 {
        fn from(x: usize) -> Self {
            ModU32::from(x as u64)
        }
    }

    impl Into<i32> for ModU32 {
        fn into(self) -> i32 {
            self.0 as i32
        }
    }

    impl Into<i64> for ModU32 {
        fn into(self) -> i64 {
            self.0 as i64
        }
    }

    impl Into<u32> for ModU32 {
        fn into(self) -> u32 {
            self.0
        }
    }

    impl Into<u64> for ModU32 {
        fn into(self) -> u64 {
            self.0 as u64
        }
    }

    impl Into<usize> for ModU32 {
        fn into(self) -> usize {
            self.0 as usize
        }
    }

    impl std::fmt::Display for ModU32 {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl std::ops::Add<ModU32> for ModU32 {
        type Output = ModU32;

        fn add(self, rhs: ModU32) -> Self::Output {
            (self.0 as u64 + rhs.0 as u64).into()
        }
    }

    impl std::ops::AddAssign<ModU32> for ModU32 {
        fn add_assign(&mut self, rhs: ModU32) {
            self.0 = (*self + rhs).0
        }
    }

    impl std::ops::Sub<ModU32> for ModU32 {
        type Output = ModU32;

        fn sub(self, rhs: ModU32) -> Self::Output {
            (if self.0 < rhs.0 {
                self.0 + (MODP - rhs.0)
            } else {
                self.0 - rhs.0
            })
            .into()
        }
    }

    impl std::ops::SubAssign<ModU32> for ModU32 {
        fn sub_assign(&mut self, rhs: ModU32) {
            self.0 = (*self - rhs).0
        }
    }

    impl std::ops::Mul<ModU32> for ModU32 {
        type Output = ModU32;

        fn mul(self, rhs: ModU32) -> Self::Output {
            Self::new((self.0 as u64) * (rhs.0 as u64))
        }
    }

    impl std::ops::MulAssign<ModU32> for ModU32 {
        fn mul_assign(&mut self, rhs: ModU32) {
            self.0 = (*self * rhs).0
        }
    }

    impl std::ops::Div<ModU32> for ModU32 {
        type Output = ModU32;

        fn div(self, rhs: ModU32) -> Self::Output {
            self * rhs.inv()
        }
    }

    impl std::ops::DivAssign<ModU32> for ModU32 {
        fn div_assign(&mut self, rhs: ModU32) {
            self.0 = (*self / rhs).0
        }
    }
}

mod mod_combin {
    use super::mod_u32::ModU32;

    pub struct ModCombin {
        factv: Vec<ModU32>,
        finvv: Vec<ModU32>,
    }

    impl ModCombin {
        pub fn new(max: usize) -> Self {
            let mut factv: Vec<ModU32> = vec![0.into(); max + 1];
            let mut finvv: Vec<ModU32> = vec![0.into(); max + 1];
            factv[0] = 1.into();
            for i in 1..=max {
                factv[i] = factv[i - 1] * (i as i64).into();
            }
            finvv[max] = factv[max].inv();
            for i in (1..=max).rev() {
                finvv[i - 1] = finvv[i] * (i as i64).into();
            }
            Self { factv, finvv }
        }

        pub fn combination(&self, n: usize, r: usize) -> ModU32 {
            if n < r {
                return 0.into();
            }
            self.factv[n] * self.finvv[r] * self.finvv[n - r]
        }
    }
}
*/

fn main() {
    let exe = "/tmp/bin21FDD20F";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";