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<bits/stdc++.h>
using namespace std;
int main(){
    int X,Y;
    cin >> X >> Y;

    int Z = max(X,Y);
    int W = min(X,Y);

    int ans = 0;

    vector<int> A;

    if(Z%2 == 0){
        int d = 1;
        for(int i=Z/2;i>=0;i--){
            int tmp = Z/2 - i + 2*i;
            if(i + 2*tmp == W){
                d = 1;
                for(int j=(i+tmp);j>i;i--){
                    d *= j;
                }
                for(int j = tmp;j>=1;j--){
                    d /= j;
                }
            }
            A.push_back(d);
        }
    }else{
        int d = 1;
        for(int i=Z/2;i>=0;i--){
            int tmp = Z/2 - i + 2*i;
            if(i + 2*tmp + 2 == W){
                d = 1;
                for(int j=(i+tmp);j>i;i--){
                    d *= j;
                }
                for(int j = tmp;j>=1;j--){
                    d /= j;
                }
            }
            A.push_back(d);
        }
    }

    for(int i=0;i<A.size();i++){
        ans += A[i]%1000000007;
    }

    cout << ans%1000000007 << endl;



    return 0;
}