#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod=1000000007;
const int nmax=1000010;
ll fac[nmax],finv[nmax],inv[nmax];
 
void COMinit(){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<nmax;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(int n,int k){
  if(n<k||n<0||k<0){
    return 0;
  }
  return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
}
 
int main(){
  COMinit();
  ll x,y;cin >> x >> y;
  ll t=abs(x-y);
  if((min(x,y)-t)%3!=0){
    cout << 0 << endl;
  }
  else{
    ll k=(min(x,y)-t)/3;
    cout << com(t+k*2,k) << endl;
  }
}
### Prompt

Generate 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;
typedef long long ll;
const int mod=1000000007;
const int nmax=1000010;
ll fac[nmax],finv[nmax],inv[nmax];
 
void COMinit(){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<nmax;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(int n,int k){
  if(n<k||n<0||k<0){
    return 0;
  }
  return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
}
 
int main(){
  COMinit();
  ll x,y;cin >> x >> y;
  ll t=abs(x-y);
  if((min(x,y)-t)%3!=0){
    cout << 0 << endl;
  }
  else{
    ll k=(min(x,y)-t)/3;
    cout << com(t+k*2,k) << endl;
  }
}
```