#include <bits/stdc++.h>
using namespace std;
#define all(V) V.begin(),V.end()
#define ll long long
#define MOD 1000000007

ll modpow(ll x, ll y) {
	ll ans = 1;
	while (y) {
		if (y & 1) {
			ans *= x;
		}
		y >>= 1;
		x *= x;
		x %= MOD;
		ans %= MOD;
	}
	return ans;
}

ll moddiv(ll x, ll y) {
	return (x * modpow(y, MOD - 2)) % MOD;
}

int main() {
	ll X, Y;
	cin >> X >> Y;
	if (X > 2 * Y) {
		cout << 0 << endl;
		return 0;
	}
	if (Y > 2 * X) {
		cout << 0 << endl;
		return 0;
	}
	ll b = 2 * X - Y;
	if (b % 3) {
		cout << 0 << endl;
		return 0;
	}
	b /= 3;
	ll a = X - 2 * b;
	//a+bCb

	ll ans = 1;
	for (ll i = 1;i <= b;i++) {
		ans *= moddiv(a + b + 1 - i, i);
		ans %= MOD;
	}
	cout << ans << endl;
}
### Prompt

Generate 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 <bits/stdc++.h>
using namespace std;
#define all(V) V.begin(),V.end()
#define ll long long
#define MOD 1000000007

ll modpow(ll x, ll y) {
	ll ans = 1;
	while (y) {
		if (y & 1) {
			ans *= x;
		}
		y >>= 1;
		x *= x;
		x %= MOD;
		ans %= MOD;
	}
	return ans;
}

ll moddiv(ll x, ll y) {
	return (x * modpow(y, MOD - 2)) % MOD;
}

int main() {
	ll X, Y;
	cin >> X >> Y;
	if (X > 2 * Y) {
		cout << 0 << endl;
		return 0;
	}
	if (Y > 2 * X) {
		cout << 0 << endl;
		return 0;
	}
	ll b = 2 * X - Y;
	if (b % 3) {
		cout << 0 << endl;
		return 0;
	}
	b /= 3;
	ll a = X - 2 * b;
	//a+bCb

	ll ans = 1;
	for (ll i = 1;i <= b;i++) {
		ans *= moddiv(a + b + 1 - i, i);
		ans %= MOD;
	}
	cout << ans << endl;
}
```