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

const long int mod=1e9+7;
long modpow(long x, long n){
    long res=1;
    for(; n>0; n>>=1) {
        if (n&1) res=res*x%mod;
        x=x*x%mod;
    }
    return res;
}
long nCr(long n, long r){
    long res=1;
    for(long int i=0; i<r; ++i) res=res*(n-i)%mod;
    for(long int i=1; i<=r; ++i) res=res*modpow(i, mod-2)%mod;
    return res;
}
int main(){
    long int X,Y;
    cin >> X >> Y;
    if((X+Y)%3!=0)cout << 0 << endl;
    else{
        long int dev = 3;
        long int num = (X+Y)/dev;
        long int x = X-num;
        long int y = Y-num;
        if(x<0 || y<0)cout << 0 << endl;
        else{cout << nCr(num,x)<<endl;}
    }
}
### Prompt

Please create a solution in CPP 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;

const long int mod=1e9+7;
long modpow(long x, long n){
    long res=1;
    for(; n>0; n>>=1) {
        if (n&1) res=res*x%mod;
        x=x*x%mod;
    }
    return res;
}
long nCr(long n, long r){
    long res=1;
    for(long int i=0; i<r; ++i) res=res*(n-i)%mod;
    for(long int i=1; i<=r; ++i) res=res*modpow(i, mod-2)%mod;
    return res;
}
int main(){
    long int X,Y;
    cin >> X >> Y;
    if((X+Y)%3!=0)cout << 0 << endl;
    else{
        long int dev = 3;
        long int num = (X+Y)/dev;
        long int x = X-num;
        long int y = Y-num;
        if(x<0 || y<0)cout << 0 << endl;
        else{cout << nCr(num,x)<<endl;}
    }
}
```