#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MOD = 1e9+7;
int modinv(int t) {
	int cur = 1, mult = t, p = MOD-2;
	while(p) {
		if(p&1) cur *= mult;
		mult *= mult;
		cur %= MOD;
		mult %= MOD;
		p /= 2;
	}
	return cur;
}
int32_t main() {
	ios::sync_with_stdio(0);cin.tie(0);
	int n, m;
	cin >> n >> m;
	if((n+m)%3) {
		return !(cout << 0);
	}
	int t = (n+m)/3;
	n -= t, m -= t;
	if(n < 0 || m < 0)
		return !(cout << 0);
	vector<int> dp(1000001);
	dp[0] = 1;
	for(int i=1; i<1000001; i++) {
		dp[i] = (dp[i-1]*i)%MOD;
	}
	cout << (((dp[n+m]*modinv(dp[n]))%MOD)*modinv(dp[m]))%MOD;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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 int long long
const int MOD = 1e9+7;
int modinv(int t) {
	int cur = 1, mult = t, p = MOD-2;
	while(p) {
		if(p&1) cur *= mult;
		mult *= mult;
		cur %= MOD;
		mult %= MOD;
		p /= 2;
	}
	return cur;
}
int32_t main() {
	ios::sync_with_stdio(0);cin.tie(0);
	int n, m;
	cin >> n >> m;
	if((n+m)%3) {
		return !(cout << 0);
	}
	int t = (n+m)/3;
	n -= t, m -= t;
	if(n < 0 || m < 0)
		return !(cout << 0);
	vector<int> dp(1000001);
	dp[0] = 1;
	for(int i=1; i<1000001; i++) {
		dp[i] = (dp[i-1]*i)%MOD;
	}
	cout << (((dp[n+m]*modinv(dp[n]))%MOD)*modinv(dp[m]))%MOD;
}
```