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

const int MAX=2000005;
const int MOD=1000000007; 

long long fac[MAX],finv[MAX], inv[MAX];

void combit() {
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    for(int i=2; i<MAX; i++){
        fac[i]=fac[i-1]*i%MOD;
        inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
        finv[i]=finv[i-1]*inv[i]%MOD;
    }
}

long long com(int nn, int kk){
    if(nn<kk) return 0;
    if(nn<0 || kk<0) return 0;
    return fac[nn]*(finv[kk]*finv[nn-kk]%MOD)%MOD;
}

int main() {
    long long x,y;
    cin >> x >> y;
    combit();
    if((x+y)%3!=0) cout << 0;
    else cout << com((x+y)/3, min(x,y)-(x+y)/3);
}
### 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;

const int MAX=2000005;
const int MOD=1000000007; 

long long fac[MAX],finv[MAX], inv[MAX];

void combit() {
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    for(int i=2; i<MAX; i++){
        fac[i]=fac[i-1]*i%MOD;
        inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
        finv[i]=finv[i-1]*inv[i]%MOD;
    }
}

long long com(int nn, int kk){
    if(nn<kk) return 0;
    if(nn<0 || kk<0) return 0;
    return fac[nn]*(finv[kk]*finv[nn-kk]%MOD)%MOD;
}

int main() {
    long long x,y;
    cin >> x >> y;
    combit();
    if((x+y)%3!=0) cout << 0;
    else cout << com((x+y)/3, min(x,y)-(x+y)/3);
}
```