//Author: Fuadul Hasan(fuadul202@gmail.com)
#include<bits/stdc++.h>
using namespace std;

#define ll long long
const int N   = 1e6 + 5;
const int M   = 1e9 + 7;
ll F[N],G[N];

ll power_mod(ll a,ll n){
	ll ret = 1;
	while(n){

		if(n&1) ret = ret * a % M;
		a = a*a%M;

		n>>=1;
	}
	return ret;
}

int main(){
	
	F[0] = G[0] = 1;
	for(int i=1;i<N;i++){
		F[i] = F[i-1] * i % M;
		G[i] = power_mod(F[i],M - 2);
	}

	int x,y;
	cin>>x>>y;
	if((x+y)%3){
		cout<<0<<endl;
		return 0;
	}
	int n = (x+y)/3;
	int u = x - n,v = y - n;
	if(u<0 or v<0){
		cout<<0<<endl;
		return 0;
	}


	ll ret = F[n] * G[u] % M * G[v]%M;

	cout<<ret<<endl;
	

	return 0;
}
### Prompt

Please formulate 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
//Author: Fuadul Hasan(fuadul202@gmail.com)
#include<bits/stdc++.h>
using namespace std;

#define ll long long
const int N   = 1e6 + 5;
const int M   = 1e9 + 7;
ll F[N],G[N];

ll power_mod(ll a,ll n){
	ll ret = 1;
	while(n){

		if(n&1) ret = ret * a % M;
		a = a*a%M;

		n>>=1;
	}
	return ret;
}

int main(){
	
	F[0] = G[0] = 1;
	for(int i=1;i<N;i++){
		F[i] = F[i-1] * i % M;
		G[i] = power_mod(F[i],M - 2);
	}

	int x,y;
	cin>>x>>y;
	if((x+y)%3){
		cout<<0<<endl;
		return 0;
	}
	int n = (x+y)/3;
	int u = x - n,v = y - n;
	if(u<0 or v<0){
		cout<<0<<endl;
		return 0;
	}


	ll ret = F[n] * G[u] % M * G[v]%M;

	cout<<ret<<endl;
	

	return 0;
}
```