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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using static System.Math;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

public static class P
{
    public static void Main()
    {
        var xy = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var x = xy[0];
        var y = xy[1];
        if ((x + y) % 3 != 0)
        {
            Console.WriteLine(0);
            return;
        }
        var moves = (x + y) / 3;
        var xCount = x - moves;
        var yCount = y - moves;
        Console.WriteLine(Factorial(moves) / (Factorial(xCount) * Factorial(yCount)));
    }

    static List<ModInt> factorialMemo = new List<ModInt>() { 1 };
    static ModInt Factorial(int x)
    {
        for (int i = factorialMemo.Count; i <= x; i++) factorialMemo.Add(factorialMemo.Last() * i);
        return factorialMemo[x];
    }
}


struct ModInt
{
    const int MOD = 1000000007;
    const long POSITIVIZER = ((long)MOD) << 31;
    long Data;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator long(ModInt modInt) => modInt.Data;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long val) => new ModInt(val);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, int b) => new ModInt() { Data = (a.Data + b + POSITIVIZER) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, long b) => new ModInt(a.Data + b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt a, ModInt b) { long res = a.Data + b.Data; return new ModInt() { Data = res >= MOD ? res - MOD : res }; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, int b) => new ModInt() { Data = (a.Data - b + POSITIVIZER) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, long b) => new ModInt(a.Data - b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt a, ModInt b) { long res = a.Data - b.Data; return new ModInt() { Data = res < 0 ? res + MOD : res }; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, int b) => new ModInt(a.Data * b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, long b) => a * new ModInt(b);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt a, ModInt b) => new ModInt() { Data = a.Data * GetInverse(b) % MOD };
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public override string ToString() => Data.ToString();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static long GetInverse(long a)
    {
        long div, p = MOD, x1 = 1, y1 = 0, x2 = 0, y2 = 1;
        while (true)
        {
            if (p == 1) return x2 + MOD; div = a / p; x1 -= x2 * div; y1 -= y2 * div; a %= p;
            if (a == 1) return x1 + MOD; div = p / a; x2 -= x1 * div; y2 -= y1 * div; p %= a;
        }
    }
}