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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

// inputに入力データ全体が入る
function Main(input) {
	input = input.split("\n");
	var pos = input.split(" ");
        var X = parseInt( pos[0], 10 );
        var Y = parseInt( pos[0], 10 );

        if( (X+Y)%3 != 0 ){ console.log(0); return; }

        var a = (2*Y-X)/3;
        var b = Y-(2*a);

       if(a<0 || b<0){ console.log(0); return; }

       var ue = a+b;
       var sita = (a>b)? b : a;

      var ue_kaijou = 1;
      var sita_kaijou = 1;

      for( i=0; i<sita; i++0{
          ue_kaijou *= a+b-i;
          sita_kaijou *= i+1;
      }
       console.log( ue_kaijou/sita_kaijou );
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));