#include<bits/stdc++.h>
#define rep(i,n) for (int i=0; i<(n); i++)
using namespace std;
using ll = long long;
const ll mod = 1e9+7;

ll modpow(ll a, ll n) {
  ll res = 1;
  while (n > 0) {
    if (n % 2) res = res * a % mod;
    a = a * a % mod;
    n /= 2;
  }
  return res;
}

ll modcomb(ll p, ll q) {
  ll bunshi = 1, bumbo = 1;
  for (ll i = p; i > p-q; i--) bunshi = bunshi * i % mod;
  rep(i,q) bumbo = bumbo * (i+1) % mod;
  
  return bunshi * modpow(bumbo, mod-2) % mod;
}

int main() {
  ll x, y;
  cin >> x >> y;
  
  if ((x+y)%3 != 0) cout << 0 << endl;
  else {
    ll n = (2*y-x)/3;
    ll m = (2*x-y)/3;
    if (n < 0 || m < 0) cout << 0 << endl;
    else cout << modcomb(n+m, min(n,m)) << endl;
  }
}
### Prompt

Develop a solution in cpp to the problem described below:

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>
#define rep(i,n) for (int i=0; i<(n); i++)
using namespace std;
using ll = long long;
const ll mod = 1e9+7;

ll modpow(ll a, ll n) {
  ll res = 1;
  while (n > 0) {
    if (n % 2) res = res * a % mod;
    a = a * a % mod;
    n /= 2;
  }
  return res;
}

ll modcomb(ll p, ll q) {
  ll bunshi = 1, bumbo = 1;
  for (ll i = p; i > p-q; i--) bunshi = bunshi * i % mod;
  rep(i,q) bumbo = bumbo * (i+1) % mod;
  
  return bunshi * modpow(bumbo, mod-2) % mod;
}

int main() {
  ll x, y;
  cin >> x >> y;
  
  if ((x+y)%3 != 0) cout << 0 << endl;
  else {
    ll n = (2*y-x)/3;
    ll m = (2*x-y)/3;
    if (n < 0 || m < 0) cout << 0 << endl;
    else cout << modcomb(n+m, min(n,m)) << endl;
  }
}
```