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<iostream>
using namespace std;
#include<vector>
 
/* This function calculates (a^b)%MOD */
long long pow(int a, int b, int MOD)
{
long long x=1,y=a; 
while(b > 0)
{
if(b%2 == 1)
{
x=(x*y);
if(x>MOD) x%=MOD;
}
y = (y*y);
if(y>MOD) y%=MOD; 
b /= 2;
}
return x;
}
 
/* Modular Multiplicative Inverse
Using Euler's Theorem
a^(phi(m)) = 1 (mod m)
a^(-1) = a^(m-2) (mod m) */
long long InverseEuler(int n, int MOD)
{
return pow(n,MOD-2,MOD);
}
 
long long C(int n, int r, int MOD)
{
vector<long long> f(n,1);
for (int i=2; i<=n;i++)
f[i]= (f[i-1]*i) % MOD;
return (f[n]*((InverseEuler(f[r], MOD) * InverseEuler(f[n-r], MOD)) % MOD)) % MOD;
}
 
int main()
{    
	int x,y;
  	cin>>x>>y;
  	int sum = x + y;
  	if(sum % 3 != 0){
      cout<<0;
      return 0;
    }
  	
  	int n = sum/3;
  	int r = y - n;
  	int p = 1000000007;
  	cout<<C(n, r, p);
}