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<bits/stdc++.h>
using namespace std;
#define ll long long
#define M 1000000007
#define ff first
#define ss second
#define mp make_pair
#define pb push_back
#define io ios_base::sync_with_stdio(false);cin.tie(NULL);
#define loop(i,n) for(int i=0;i<n;i++)
long int fact(int x)
{   long int p=1;
    loop(i,x)
     p=p*(i+1)%M;
    return p;
}
void solve()
{
    int x,y,m,n;
    ll t=0,s=0;
    cin>>x>>y;
    double p,q;
    p=(2*y-x)/3;
    q=(2*x-y)/3;
    m=(2*y-x)/3;
    n=(2*x-y)/3;
    if(p==m && q==n)
    {
        t=fact(m+n)/fact(m)/fact(n);
       // cout<<m<<n;
       cout<<t;
    }
    else
    cout<<"0";
    // loop(i,y+1)
    // {
    //     q=(y-i)/2;
    //     if(q==(double)i)
    //     s=(s+1)%M;
    // }
    // ll z=(fact(x)/fact(2*t)/fact(x-2*t))%M;
    // ll w=(fact(y)/fact(2*s)/fact(x-2*s))%M;
    // cout<<(q*z)%M;
}
int main() {
	// your code goes here
// 	int t ;
// 	cin>>t;
// 	while(t--)
    solve();
	return 0;
}