#include <bits/stdc++.h>
using namespace std;

using ll=long long;
const int mod=1e9+7;

ll modinv(ll a, ll m) {
  ll b=m, u=1, v=0;
  while(b) {
    ll t=a/b;
    a -= t*b; swap(a, b);
    u -= t*v; swap(u, v);
  }
  u %= m;
  if(u<0)
    u += m;
  return u;
}
 
ll cmb(ll n, ll k) {
    ll i;
    if(k>n-k)
        k = n-k;
    ll r1=1, r2=1;
    for(i=n; i>n-k; i--)
        r1 = r1*i%mod;
    for(i=1; i<=k; i++)
        r2 = r2*i%mod;
    return r1 * modinv(r2,mod) % mod;
}

int main() {
    ll X,Y;
    cin >> X >> Y;

    if((X+Y)%3==0 && X-(X+Y)/3>=0 && Y-(X+Y)/3>=0) {
        cout << cmb((X+Y)/3, X-(X+Y)/3) << endl;
    } else {
        cout << 0 << 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 int mod=1e9+7;

ll modinv(ll a, ll m) {
  ll b=m, u=1, v=0;
  while(b) {
    ll t=a/b;
    a -= t*b; swap(a, b);
    u -= t*v; swap(u, v);
  }
  u %= m;
  if(u<0)
    u += m;
  return u;
}
 
ll cmb(ll n, ll k) {
    ll i;
    if(k>n-k)
        k = n-k;
    ll r1=1, r2=1;
    for(i=n; i>n-k; i--)
        r1 = r1*i%mod;
    for(i=1; i<=k; i++)
        r2 = r2*i%mod;
    return r1 * modinv(r2,mod) % mod;
}

int main() {
    ll X,Y;
    cin >> X >> Y;

    if((X+Y)%3==0 && X-(X+Y)/3>=0 && Y-(X+Y)/3>=0) {
        cout << cmb((X+Y)/3, X-(X+Y)/3) << endl;
    } else {
        cout << 0 << endl;
    }
}
```