#include <iostream>
#include <cstdio>
#define N 2000005
using namespace std;

typedef long long ll;
ll M = 1e9 + 7;
ll x, y, fac[N] = {1,1}, inv[N] = {1,1}, fiv[N] = {1,1};
int main()
{
	ll i, t;
	cin >> x >> y;
	for (i = 2; i < N; i++) {
		fac[i] = fac[i - 1] * i % M;
		inv[i] = inv[M % i] * (M - M / i) % M;
		fiv[i] = fiv[i - 1] * inv[i] % M;
	}
	if ((x + y) % 3) {puts("0"); return 0;}
	t = (x + y) / 3;
    x -= t; y -= t;
    if (x < 0 || y < 0) {puts("0"); return 0;}
    cout << fac[x + y] * fiv[x] % M * fiv[y] % M << endl;
    return 0;
}
### 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 <iostream>
#include <cstdio>
#define N 2000005
using namespace std;

typedef long long ll;
ll M = 1e9 + 7;
ll x, y, fac[N] = {1,1}, inv[N] = {1,1}, fiv[N] = {1,1};
int main()
{
	ll i, t;
	cin >> x >> y;
	for (i = 2; i < N; i++) {
		fac[i] = fac[i - 1] * i % M;
		inv[i] = inv[M % i] * (M - M / i) % M;
		fiv[i] = fiv[i - 1] * inv[i] % M;
	}
	if ((x + y) % 3) {puts("0"); return 0;}
	t = (x + y) / 3;
    x -= t; y -= t;
    if (x < 0 || y < 0) {puts("0"); return 0;}
    cout << fac[x + y] * fiv[x] % M * fiv[y] % M << endl;
    return 0;
}
```