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

typedef long long ll;

const ll MOD = 1000000007;

int mpow(ll a, ll b) {
    ll c = 1;
    while (b) {
        if (b % 2) c = c*a%MOD;
        b/=2;
        a = a*a%MOD;
    }
    return c;
}

int C (ll a, ll b) {
    ll nume = 1;
    for (int i = a; i > a-b; i--) {
        nume = nume*i%MOD;
    }
    ll deno = 1;
    for (int i = 2; i <= b; i++) {
        deno = deno*i%MOD;
    }
    return nume*mpow(deno, MOD-2) % MOD;
}

int main() {
    int x, y;
    cin >> x >> y;
    int a = (x+y)/3;
    int b = x-a;
    int c = y-a;
    if ((x+y)%3 != 0 || b < 0 || c < 0) {
        cout << 0 << endl;
        return 0;
    }
    cout << C(b+c, b) << endl;
    return 0;
}

### 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;

typedef long long ll;

const ll MOD = 1000000007;

int mpow(ll a, ll b) {
    ll c = 1;
    while (b) {
        if (b % 2) c = c*a%MOD;
        b/=2;
        a = a*a%MOD;
    }
    return c;
}

int C (ll a, ll b) {
    ll nume = 1;
    for (int i = a; i > a-b; i--) {
        nume = nume*i%MOD;
    }
    ll deno = 1;
    for (int i = 2; i <= b; i++) {
        deno = deno*i%MOD;
    }
    return nume*mpow(deno, MOD-2) % MOD;
}

int main() {
    int x, y;
    cin >> x >> y;
    int a = (x+y)/3;
    int b = x-a;
    int c = y-a;
    if ((x+y)%3 != 0 || b < 0 || c < 0) {
        cout << 0 << endl;
        return 0;
    }
    cout << C(b+c, b) << endl;
    return 0;
}

```