#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
ll mod=1e9+7;
ll inv(ll a){
    ll n=mod-2,ans=1;
    while(n>0){
        if(n%2) ans=ans*a%mod;
        n=n/2;
        a=a*a%mod;
    }
    return ans;
}
ll A[2000001];
ll nCr(ll n,ll r){
    return A[n]*inv(A[r])%mod*inv(A[n-r])%mod;
}
int main(){
    ll x,y;
    cin>>x>>y;
    if((x+y)%3){cout<<0;return 0;}
    ll k=(2*y-x)/3,l=(2*x-y)/3;
    if(k<0||l<0){cout<<0;return 0;}
    A[0]=1;
    rep(i,2000000) A[i+1]=A[i]*(i+1)%mod;
    cout<<nCr(k+l,l);
}
### 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;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
ll mod=1e9+7;
ll inv(ll a){
    ll n=mod-2,ans=1;
    while(n>0){
        if(n%2) ans=ans*a%mod;
        n=n/2;
        a=a*a%mod;
    }
    return ans;
}
ll A[2000001];
ll nCr(ll n,ll r){
    return A[n]*inv(A[r])%mod*inv(A[n-r])%mod;
}
int main(){
    ll x,y;
    cin>>x>>y;
    if((x+y)%3){cout<<0;return 0;}
    ll k=(2*y-x)/3,l=(2*x-y)/3;
    if(k<0||l<0){cout<<0;return 0;}
    A[0]=1;
    rep(i,2000000) A[i+1]=A[i]*(i+1)%mod;
    cout<<nCr(k+l,l);
}
```