#include<bits/stdc++.h>
using namespace std;
long long md=1e9+7;
long long f(int a){
	long long rez=1;
	for(int i = 1 ; i <= a ; i ++)
		rez=rez*i%md;
	return rez;
}
long long pw(int a,int b){
	if(b==0)return 1;
	if(b==1)return a;
	long long g=pw(a,b/2);
	g=g*g%md;
	if(b%2)return g*a%md;
	return g;
}
long long cmb(int c,int k){
	long long fu=f(c);
	long long fd=pw(f(k)*f(c-k)%md,md-2);
	return fu*fd%md;
}
int main(){
	int x,y;
	cin>>x>>y;
	int a=(2*y-x);
	int b=(2*x-y);
	if(a%3||b%3||(x+y)%3||a<0||b<0){
		cout<<0;
		return 0;
	}
	a/=3;b/=3;
	// cout<<a<<" "<<b<<endl;
	cout<<cmb(a+b,a);
}
### Prompt

Generate a Cpp solution to the following problem:

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;
long long md=1e9+7;
long long f(int a){
	long long rez=1;
	for(int i = 1 ; i <= a ; i ++)
		rez=rez*i%md;
	return rez;
}
long long pw(int a,int b){
	if(b==0)return 1;
	if(b==1)return a;
	long long g=pw(a,b/2);
	g=g*g%md;
	if(b%2)return g*a%md;
	return g;
}
long long cmb(int c,int k){
	long long fu=f(c);
	long long fd=pw(f(k)*f(c-k)%md,md-2);
	return fu*fd%md;
}
int main(){
	int x,y;
	cin>>x>>y;
	int a=(2*y-x);
	int b=(2*x-y);
	if(a%3||b%3||(x+y)%3||a<0||b<0){
		cout<<0;
		return 0;
	}
	a/=3;b/=3;
	// cout<<a<<" "<<b<<endl;
	cout<<cmb(a+b,a);
}
```