#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll mod=1e9+7;
ll yojo(ll x){
	ll num=1;
	for(int i=1;i<=x;i++){
		num*=i;
		num%=mod;
	}
	return num;
}
ll r(ll x){
	ll yan=1e9+5;
		ll tama=1;
		while(yan>0){
			if(yan%2)tama=(tama*x)%mod;
			x=(x*x)%mod;
			yan/=2;
		}
		tama%=mod;
		return tama;
}
int main(){
	ll x,y,ans=1;
	cin>>x>>y;
	if(x<y)swap(x,y);
	if((x+y)%3)ans=0;
	else{
		ll k=(2*y-x)/3,l=(2*x-y)/3;
		if(k<0||l<0){
			cout<<0;
			return 0;
		}
		ll p[2]={yojo(k),yojo(l)};
		ans=yojo(k+l);
		ans%=mod;
		ans*=r(p[0]);
		ans%=mod;
		ans*=r(p[1]);
		ans%=mod;
	}
	cout<<ans;

	return 0;
}

### Prompt

Please create a solution in Cpp 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;
typedef long long ll;
ll mod=1e9+7;
ll yojo(ll x){
	ll num=1;
	for(int i=1;i<=x;i++){
		num*=i;
		num%=mod;
	}
	return num;
}
ll r(ll x){
	ll yan=1e9+5;
		ll tama=1;
		while(yan>0){
			if(yan%2)tama=(tama*x)%mod;
			x=(x*x)%mod;
			yan/=2;
		}
		tama%=mod;
		return tama;
}
int main(){
	ll x,y,ans=1;
	cin>>x>>y;
	if(x<y)swap(x,y);
	if((x+y)%3)ans=0;
	else{
		ll k=(2*y-x)/3,l=(2*x-y)/3;
		if(k<0||l<0){
			cout<<0;
			return 0;
		}
		ll p[2]={yojo(k),yojo(l)};
		ans=yojo(k+l);
		ans%=mod;
		ans*=r(p[0]);
		ans%=mod;
		ans*=r(p[1]);
		ans%=mod;
	}
	cout<<ans;

	return 0;
}

```