#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll M=1e9+7;
ll inv(ll a){
	return a==1?1:(ll)(M-M/a)*inv(M%a)%M;
}
void C(int r,int n){
	if(r>n-r) r=n-r;
	ll a1=1,a2=1;
	for(int i=0;i<r;i++){
		a1=a1*(n-i)%M;
		a2=a2*(i+1)%M;
	}
	cout << a1*inv(a2)%M << endl;
}
int main(){
	ll a,b;
	cin >> a >> b;
	if((a+b)%3!=0)
	cout << 0 << endl;
	else{
		ll x=(a+b)/3*2-a,y=a-(a+b)/3;
		if(x<0||y<0){
			cout << 0 << endl;
		}
		else{
			C(x,x+y);
		}
	}
	return 0;
}
### Prompt

In CPP, your task is to solve 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;
typedef long long ll;
const ll M=1e9+7;
ll inv(ll a){
	return a==1?1:(ll)(M-M/a)*inv(M%a)%M;
}
void C(int r,int n){
	if(r>n-r) r=n-r;
	ll a1=1,a2=1;
	for(int i=0;i<r;i++){
		a1=a1*(n-i)%M;
		a2=a2*(i+1)%M;
	}
	cout << a1*inv(a2)%M << endl;
}
int main(){
	ll a,b;
	cin >> a >> b;
	if((a+b)%3!=0)
	cout << 0 << endl;
	else{
		ll x=(a+b)/3*2-a,y=a-(a+b)/3;
		if(x<0||y<0){
			cout << 0 << endl;
		}
		else{
			C(x,x+y);
		}
	}
	return 0;
}
```