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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
void con(vector<vector<int>> &v){
    for(int i = 0;i <v.size(); i++){
    v[i][0]=1;
    v[i][i]=1;
  }
  for(int k = 1;k <v.size();k++){
    for(int j = 1;j<k;j++){
      v[k][j]=(v[k-1][j-1]+v[k-1][j])%1000000007;
    }
  }
}
int main() {
  long long count=0;
  int X,Y,N;
  cin>>X>>Y;
  if((X+Y)%3==0){
    N=(X+Y)/3;
    X-=N;
    Y-=N;
    if(X<Y){
      int a=X;
      X=Y;
      Y=a;
    }
    vector<vector<int>> v(Y+1,vector<int>(Y+1,0));
    con(v);
    cout<<v[Y][X];
  }
  else cout<<0;
}