#include<bits/stdc++.h>

int main(){
    using namespace std;
    unsigned long X, Y;
    cin >> X >> Y;
    if((X + Y) % 3)return 0 & puts("0");
    {
        unsigned long k{(X + Y) / 3};
        if(X < k || Y < k)return 0 & puts("0");
        X -= k;
        Y -= k;
    }
    unsigned long N{X + Y}, d{1}, n{1};
    constexpr unsigned long MOD = 1000000007;
    for(unsigned long i = 0, j = N; i < X;){
        (d *= j--) %= MOD;
        (n *= ++i) %= MOD;
    }
    unsigned long a{MOD - 2};
    while(a){
        if(a & 1)(d *= n) %= MOD;
        (n *= n) %= MOD;
        a >>= 1;
    }
    cout << d << endl;
    return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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>

int main(){
    using namespace std;
    unsigned long X, Y;
    cin >> X >> Y;
    if((X + Y) % 3)return 0 & puts("0");
    {
        unsigned long k{(X + Y) / 3};
        if(X < k || Y < k)return 0 & puts("0");
        X -= k;
        Y -= k;
    }
    unsigned long N{X + Y}, d{1}, n{1};
    constexpr unsigned long MOD = 1000000007;
    for(unsigned long i = 0, j = N; i < X;){
        (d *= j--) %= MOD;
        (n *= ++i) %= MOD;
    }
    unsigned long a{MOD - 2};
    while(a){
        if(a & 1)(d *= n) %= MOD;
        (n *= n) %= MOD;
        a >>= 1;
    }
    cout << d << endl;
    return 0;
}
```