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: Accepted)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define MOD 1000000007
vector<ll> fact(1000000);
void init_fact(int n){
	fact[0]=1;
	for (int i = 1; i < n+1; i++){
		fact[i]=fact[i-1]*i;
		fact[i]%=MOD;
	}
}

ll mod_pow(ll x, ll p){
	ll res=1;
	ll n=x;
	while(p>0){
		if(p&1==1)res=(res*n)%MOD;
		n=(n*n)%MOD;
		p=(p>>1);
	}
	return res;
}
ll nCr(int n, int r){
	ll res=1;
	res*=fact[n];
	res*=mod_pow(fact[r],MOD-2);
	res%=MOD;
	res*=mod_pow(fact[n-r],MOD-2);
	res%=MOD;
	return res;
}
int main() {
    int X,Y; cin>>X>>Y;
    if((X+Y)%3!=0){
        cout<<0<<endl;
        return 0;
    }
    int n=(X+Y)/3;
    int a=2*n-X;
    int b=n-a;
    init_fact(n);
    if(a<0 || b<0){
        cout<<0<<endl;
        return 0;
    }
    cout<<nCr(n,a)<<endl;
}