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 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
using lint = long int;
using P = pair<lint, lint>;
#define MOD 1000000007

lint X, Y;

lint factorial(lint n){
  	lint res = 1;
  	for(lint i = 2; i <= n; i++){ res *= i; res %= MOD; }
  	return res;
}


/*逆元導出*/
lint inv_mod(lint x, lint y){
  	lint a = x, b = y, u = 1, v = 0;
  	lint d;
  	while(b){
    	d = a / b;
      	a -= b * d; swap(a, b);
      	u -= v * d; swap(u, v);
    }
  
  	u %= y;
  	if(u < 0) u += y;
  	return u;
}



lint Comb(lint n, lint r){
  	if(n < 1) return 0;
  	lint res = 1, div = 1;
  	for(lint i = 0; i < r; i++){ 
      	res *= (n-i); res %= MOD;
      	div *= (i+1); div %= MOD;
    }
  	res = (res * inv_mod(div, MOD)) % MOD;
  	return res;
}



P identif_pos(lint x, lint y){
    lint a = (2*x-y)/3, b = (2*y-x)/3;
    if(3*a != 2*x-y || 3*b != 2*y-x) return {-1, -1};
    else return {a, b};
}


int main(){
    cin >> X >> Y;
  	P p = identif_pos(X, Y);
    cout << Comb(p.first+p.second, p.first) << endl;
    return 0;
}