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

#include <bits/stdc++.h>
typedef long long int ll;
using namespace std;
const ll N = 2000009;
const ll p = 31;
const ll m = 1e9 + 7;
const ll inf= 1e14;
ll mod = 1e9+7;
ll powm(ll a, ll b) { ll res = 1; while (b) { if (b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1; } return res; }
ll fact[N];


ll ncr(ll n,ll r){
     return (((fact[n]*powm(fact[r],mod-2))%mod)*powm(fact[n-r],mod-2))%mod;
}
 int main() {   
     ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    fact[0] =1;
    for(ll i = 1;i<N;i++){
     fact[i] = (fact[i-1]*i)%mod;
    }
     // #ifndef ONLINE_JUDGE
     // freopen("input.txt", "r", stdin);
     // freopen("output.txt", "w", stdout);
     // #endif
     ll t = 1;
     // cin>>t;
     while(t--){
          ll x,y;cin>>x>>y;
          // cout<<x<<y;
          ll ans = 0;
          ll a = (2*x - y)/3;
          ll b = (2*y - x)/3;

          if(x== 2*a + b && y == 2*b + a && a>0 && b>0){
               ans=ncr(a+b,a);
          }
          cout<<ans%mod;
     }
}