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: Wrong Answer)

using System;
class abc145_d{
  public static void Main(){
    String[] str = Console.ReadLine().Split(' ');
    int x = int.Parse(str[0]);
    int y = int.Parse(str[1]);
    //long div = 1000000007;
    int px = 0;
    int py = 0;
    ulong countx=0;
    ulong county=0;
    bool flag = false;
    while(px<=x && py<=y){
      if(px == x && py == y){
        flag = true;
        break;
      }
      else{
        if(Math.Abs(x-px) <= Math.Abs(y-py)){
          py+=2;
          px+=1;
          county++;
        }
        else{
          px+=2;
          py+=1;
          countx++;
        }
      }
    }
    //long[,] data = new long[countx+county+1,countx+county+1];
    /*for(long i=0; i<=countx+county; i++){
      for(long j=0; j<=countx+county; j++){
        data[i,j] = -1;
      }
    }*/
    ulong ans = 0;
    if(flag){
      ans = (nCr(countx+county, countx/*, ref data*/))%1000000007;
    }
    Console.WriteLine(ans);
  }

  public static ulong nCr(ulong n, ulong m/*, ref long[,] data*/){
    ulong ret=1;
    /*ret = fact(n)/fact(m);
    return ret;*/
    for(ulong i=n; i>=m; i--){
      ret = (ret * i) % (ulong)(Math.Pow(10,9)+7);
      //Console.WriteLine("ret = {0}",ret);
    }
    //Console.WriteLine("ret = {0}",ret);
    return ret;
  }
  /*public static ulong fact(ulong n){
    ulong ret = 1;
    for(ulong i=1; i<=n; i++){
      ret *= i;
    }
    return ret;
  }*/
}