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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <string>
#define rep(i, n)   for(int i = 0; i < (n); i++)
#define MOD (1e9+7)
using namespace std;
typedef long long ll;

int main(){
    int x,y;    cin >> x >> y; 
    int ans = 0;
    for(int a1 = 0; a1 <= x; a1++){
        if((x-a1)%2==0 && a1*2+(x-a1)/2 == y){
            ans++;
            ans%=(int)MOD;
        }
    }
    for(int a1 = 0; a1 <= x; a1++){
        if((y-a1)%2==0 && a1*2+(y-a1)/2 == x){
            ans++;
            ans%=(int)MOD;
        }
    }
    cout << ans << endl;
}