#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef double D;
typedef pair<ll,ll> P;
#define M 1000000007
#define F first
#define S second
#define PB push_back
#define INF 100000000000000000
ll x,y,ans=1,inv[2000005],invk[2000005],ka[2000005];
int main(void){
	cin>>x>>y;
	inv[0]=1,inv[1]=1,ka[0]=1,invk[0]=1;
	for(ll i=2;i<=x+y;i++)inv[i]=M-(M/i)*inv[M%i]%M;
	for(ll i=1;i<=x+y;i++)ka[i]=ka[i-1]*i%M,invk[i]=invk[i-1]*inv[i]%M;
	if((x+y)%3!=0)ans=0;
	ll n=(x+y)/3;
	x-=n,y-=n;
	ans=ans*ka[x+y]%M*invk[y]%M*invk[x]%M;
	cout<<ans<<endl;
}

### 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;
typedef double D;
typedef pair<ll,ll> P;
#define M 1000000007
#define F first
#define S second
#define PB push_back
#define INF 100000000000000000
ll x,y,ans=1,inv[2000005],invk[2000005],ka[2000005];
int main(void){
	cin>>x>>y;
	inv[0]=1,inv[1]=1,ka[0]=1,invk[0]=1;
	for(ll i=2;i<=x+y;i++)inv[i]=M-(M/i)*inv[M%i]%M;
	for(ll i=1;i<=x+y;i++)ka[i]=ka[i-1]*i%M,invk[i]=invk[i-1]*inv[i]%M;
	if((x+y)%3!=0)ans=0;
	ll n=(x+y)/3;
	x-=n,y-=n;
	ans=ans*ka[x+y]%M*invk[y]%M*invk[x]%M;
	cout<<ans<<endl;
}

```