#define MOD 1000000007

#include <iostream>
#include <vector>
using namespace std;

long pow(long a, long b) {
	if (!b) return 1;
	long c = pow(a, b / 2);
	if (b % 2) c = a * c % MOD * c % MOD;
	else c = c * c % MOD;
	return c;
}

int main() {
	int X, Y;
	cin >> X >> Y;
	if ((X * 2 - Y) % 3 || (Y * 2 - X) % 3) cout << 0;
	else {
		int a = (X * 2 - Y) / 3, b = (Y * 2 - X) / 3;
		if (a < 0 || b < 0) cout << 0;
		else {
			vector<long> c(a + b + 1, 1), d(a + b + 1, 1);
			for (int i = 1; i <= a + b; i++) {
				c[i] = c[i - 1] * i % MOD;
				d[i] = pow(c[i], MOD - 2);
			}
			cout << c[a + b] * d[a] % MOD * d[b] % MOD;
		}
	}
}
### Prompt

Create a solution in Cpp for 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
#define MOD 1000000007

#include <iostream>
#include <vector>
using namespace std;

long pow(long a, long b) {
	if (!b) return 1;
	long c = pow(a, b / 2);
	if (b % 2) c = a * c % MOD * c % MOD;
	else c = c * c % MOD;
	return c;
}

int main() {
	int X, Y;
	cin >> X >> Y;
	if ((X * 2 - Y) % 3 || (Y * 2 - X) % 3) cout << 0;
	else {
		int a = (X * 2 - Y) / 3, b = (Y * 2 - X) / 3;
		if (a < 0 || b < 0) cout << 0;
		else {
			vector<long> c(a + b + 1, 1), d(a + b + 1, 1);
			for (int i = 1; i <= a + b; i++) {
				c[i] = c[i - 1] * i % MOD;
				d[i] = pow(c[i], MOD - 2);
			}
			cout << c[a + b] * d[a] % MOD * d[b] % MOD;
		}
	}
}
```