#include<bits/stdc++.h>
using namespace std;
using ll=long long;
const ll MOD=1000000007;
const ll MAX=1000000;
ll fac[MAX],finv[MAX],inv[MAX];
void COMinit(){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<MAX;i++){
    fac[i]=fac[i-1]*i%MOD;
    inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
    finv[i]=finv[i-1]*inv[i]%MOD;
  }
}
ll COM(ll n, ll k){
  if(n<0||k<0)return 0;
  if(n<k)return 0;
  return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}
int main(){
ll X,Y;
cin>>X>>Y;
if((X+Y)%3!=0){
  cout<<0<<endl;
  return 0;
}
ll m=(2*X-Y)/3;
ll n=(2*Y-X)/3;
COMinit();
ll ans=COM(n+m,n)%MOD;
while(ans<0){
  ans+=MOD;
}
cout<<ans%MOD<<endl;

}
### 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
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
const ll MOD=1000000007;
const ll MAX=1000000;
ll fac[MAX],finv[MAX],inv[MAX];
void COMinit(){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<MAX;i++){
    fac[i]=fac[i-1]*i%MOD;
    inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
    finv[i]=finv[i-1]*inv[i]%MOD;
  }
}
ll COM(ll n, ll k){
  if(n<0||k<0)return 0;
  if(n<k)return 0;
  return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}
int main(){
ll X,Y;
cin>>X>>Y;
if((X+Y)%3!=0){
  cout<<0<<endl;
  return 0;
}
ll m=(2*X-Y)/3;
ll n=(2*Y-X)/3;
COMinit();
ll ans=COM(n+m,n)%MOD;
while(ans<0){
  ans+=MOD;
}
cout<<ans%MOD<<endl;

}
```