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)

"use strict";

function factorial(num) {
  if (num == 1) {
    return num;
  } else {
    return num * factorial(num - 1);
  }
}

const main = arg => {
    arg = arg.trim().split("\n");
    const X = parseInt(arg[0].split(" ")[0]);
    const Y = parseInt(arg[0].split(" ")[1]);
    
    // Xを基準で考える？
    const numOfTwo = Math.floor(X / 2);
    
    const answer = 0;
    
    for(let i=numOfTwo; i>=0; i--) {
        const numOfOne = X - (2 * i);
        
        // 到達可能である
        if(i + (2 * numOfOne) === Y) {
            // console.log("Xには2を" + numOfTwo + "個、1を" + numOfOne + "個使って到達できる")
            // console.log("Yには1を" + numOfTwo + "個、2を" + numOfOne + "個使って到達できる")
            
            //const temp1 = factorial((2 * i) + numOfOne);
            //const temp2 = factorial((2 * i)) + factorial(numOfOne);
            
            answer ++;

            // list.push(temp1 / temp2);
        }

    }
    
    if(list.length === 0) {
        console.log(0);
        return;
    }

    console.log(answer % 10e9);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));