#include <iostream>
using namespace std;

long long x, y, t = 0;
const long long M = 1000000007;
const long long N = 1000000005;

int main()
{	

	cin >> x >> y;

	if (x <= y * 2 && y <= x * 2) {
		if ((x * 2 - y) % 3 == 0 && (y * 2 - x) % 3 == 0) {
			long long a = (x * 2 - y) / 3, b = (y * 2 - x) / 3;

			t = 1;

			for (long long i = 0; i < a; i++)
				t = (t * (a + b - i)) % M;

			for (long long i = 1; i <= a; i++) {
				long long c[40];
				long long d = i;

				c[0] = i;

				for (int j = 1; (1ull << j) < N; j++) {
					c[j] = c[j - 1] * c[j - 1] % M;

					if (N & (1ull << j))
						d = (d * c[j]) % M;
				}

				t = t * d % M;
			}
		}
	}

	cout << t << 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 <iostream>
using namespace std;

long long x, y, t = 0;
const long long M = 1000000007;
const long long N = 1000000005;

int main()
{	

	cin >> x >> y;

	if (x <= y * 2 && y <= x * 2) {
		if ((x * 2 - y) % 3 == 0 && (y * 2 - x) % 3 == 0) {
			long long a = (x * 2 - y) / 3, b = (y * 2 - x) / 3;

			t = 1;

			for (long long i = 0; i < a; i++)
				t = (t * (a + b - i)) % M;

			for (long long i = 1; i <= a; i++) {
				long long c[40];
				long long d = i;

				c[0] = i;

				for (int j = 1; (1ull << j) < N; j++) {
					c[j] = c[j - 1] * c[j - 1] % M;

					if (N & (1ull << j))
						d = (d * c[j]) % M;
				}

				t = t * d % M;
			}
		}
	}

	cout << t << endl;

	return 0;
}
```