// abc145_d.cc
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const ll MOD = 1e9 + 7;

int inv(int a) {
	return a == 1 ? 1 : (long long) (MOD - MOD/a) * inv(MOD%a) % MOD;
}

ll f(ll n, ll m) {
	if (m < 0 || n < m) return 0;
	if (m > n - m) m = n - m;
	ll up = 1, down = 1;

	for (ll i = 0; i < m; i++) {
		up = up * (n-i) % MOD;
		down = down * (i+1) % MOD;
	}
	return up * inv(down) % MOD;
}

int main() {

	ll x, y; scanf("%lld%lld", &x, &y);
	if (x > y) swap(x, y);
	if ((2*y - x) % 3 == 0) {
		ll a = (2 * y - x) / 3;
		ll b = (x - a) / 2;
		printf("%lld", f(a+b, a));
	} else printf("0\n");

	return 0;
}
### Prompt

In Cpp, your task is to solve 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
// abc145_d.cc
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
const ll MOD = 1e9 + 7;

int inv(int a) {
	return a == 1 ? 1 : (long long) (MOD - MOD/a) * inv(MOD%a) % MOD;
}

ll f(ll n, ll m) {
	if (m < 0 || n < m) return 0;
	if (m > n - m) m = n - m;
	ll up = 1, down = 1;

	for (ll i = 0; i < m; i++) {
		up = up * (n-i) % MOD;
		down = down * (i+1) % MOD;
	}
	return up * inv(down) % MOD;
}

int main() {

	ll x, y; scanf("%lld%lld", &x, &y);
	if (x > y) swap(x, y);
	if ((2*y - x) % 3 == 0) {
		ll a = (2 * y - x) / 3;
		ll b = (x - a) / 2;
		printf("%lld", f(a+b, a));
	} else printf("0\n");

	return 0;
}
```