#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 4e6 + 10;
const int MOD = 1e9 + 7;
ll d[N];
ll qpow(ll x, ll k) { 
    ll r = 1;
    while(k) {
        if(k & 1) {
            r = r * x % MOD;
        }
        k >>= 1;
        x = x * x % MOD;
    }
    return r;
}
int main() {
    d[0] = 1;
    for(int i = 1; i < N; i++) {
        d[i] = d[i-1] * i % MOD;
    }
    ll a0, a1;
    cin >> a0 >> a1;
    if(2*a1 - a0 < 0 || 2*a0 - a1 < 0 || (2*a1 - a0) % 3 != 0 || (2*a0 - a1) % 3 != 0) {
        cout << 0 << endl;
        return 0;
    }
    ll x = (2*a1 - a0)/3, y = (2*a0 - a1)/3;
    cout << d[x+y] * qpow(d[x],MOD-2) % MOD * qpow(d[y], MOD-2) % MOD << endl;
    return 0;
}
### Prompt

Your task is to create 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;
typedef long long ll;
const int N = 4e6 + 10;
const int MOD = 1e9 + 7;
ll d[N];
ll qpow(ll x, ll k) { 
    ll r = 1;
    while(k) {
        if(k & 1) {
            r = r * x % MOD;
        }
        k >>= 1;
        x = x * x % MOD;
    }
    return r;
}
int main() {
    d[0] = 1;
    for(int i = 1; i < N; i++) {
        d[i] = d[i-1] * i % MOD;
    }
    ll a0, a1;
    cin >> a0 >> a1;
    if(2*a1 - a0 < 0 || 2*a0 - a1 < 0 || (2*a1 - a0) % 3 != 0 || (2*a0 - a1) % 3 != 0) {
        cout << 0 << endl;
        return 0;
    }
    ll x = (2*a1 - a0)/3, y = (2*a0 - a1)/3;
    cout << d[x+y] * qpow(d[x],MOD-2) % MOD * qpow(d[y], MOD-2) % MOD << endl;
    return 0;
}
```