#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int NN = 1e7;
const int M = 1e9+7;
int main(){
    int x,y;cin>>x>>y;
    ll N = (x+y)/3;
    ll K = (2*x-y)/3;
    vector<ll> fact(NN),ifact(NN),inv(NN);
   
    fact[0] = ifact[0] = inv[1] = fact[1] = ifact[1] = 1;
	for(int i = 2; i < NN; i++){
		fact[i] = fact[i-1]*i%M;
		inv[i] = (M-M/i*inv[M%i]%M)%M;
		ifact[i] = inv[i]*ifact[i-1]%M;
	}

    if((x+y)%3!=0) {
        cout<<0;
        return 0;
    }
  
    x-=N;
    y-=N;
    if(x<0 || y<0){
        cout<<0;
        return 0;
    }
    cout<<fact[x+y]%M*ifact[x]%M*ifact[y]%M;

}

### Prompt

Construct a CPP code solution to the problem outlined:

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.

Examples

Input

3 3


Output

2


Input

2 2


Output

0


Input

999999 999999


Output

151840682

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int NN = 1e7;
const int M = 1e9+7;
int main(){
    int x,y;cin>>x>>y;
    ll N = (x+y)/3;
    ll K = (2*x-y)/3;
    vector<ll> fact(NN),ifact(NN),inv(NN);
   
    fact[0] = ifact[0] = inv[1] = fact[1] = ifact[1] = 1;
	for(int i = 2; i < NN; i++){
		fact[i] = fact[i-1]*i%M;
		inv[i] = (M-M/i*inv[M%i]%M)%M;
		ifact[i] = inv[i]*ifact[i-1]%M;
	}

    if((x+y)%3!=0) {
        cout<<0;
        return 0;
    }
  
    x-=N;
    y-=N;
    if(x<0 || y<0){
        cout<<0;
        return 0;
    }
    cout<<fact[x+y]%M*ifact[x]%M*ifact[y]%M;

}

```