#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll mod = 1000000007;

ll rui(ll a,ll b){
    ll ans=1;
    while(b>0){
        if(b&1) ans=ans*a%mod;
        a=a*a%mod;
        b/=2;
    }
    return ans;
}

ll comb(ll a,ll b){
    ll ans=1;
    for(ll i=a;i>a-b;i--){
        ans=ans*i%mod;
    }
    for(ll i=1;i<=b;i++){
        ans=(ans*rui(i,mod-2))%mod;
    }
    return ans;
}

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

In cpp, your task is to solve 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;
ll mod = 1000000007;

ll rui(ll a,ll b){
    ll ans=1;
    while(b>0){
        if(b&1) ans=ans*a%mod;
        a=a*a%mod;
        b/=2;
    }
    return ans;
}

ll comb(ll a,ll b){
    ll ans=1;
    for(ll i=a;i>a-b;i--){
        ans=ans*i%mod;
    }
    for(ll i=1;i<=b;i++){
        ans=(ans*rui(i,mod-2))%mod;
    }
    return ans;
}

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