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

const int mod = pow(10,9)+7;

int main() {
	
	int x, y;
	cin >> x >> y;
	int k=x+y;
	bool flg = 1;
	if(k%3!=0) flg=0;
	k/=3;
	if(x<k || y<k) flg=0;
	int d = x-k;
	int ans = 0;
	if(flg && (d!=0)){
		vector<long long> inv(d+1),finv(d+1),fac(d);
		inv.at(1)=1;
		finv.at(1)=1;
		fac.at(0) = k;
		for(int i=2; i<=d; i++) inv.at(i) = mod - inv.at(mod%i) * (mod/i) %mod;
		for(int i=2; i<=d; i++) finv.at(i) = finv.at(i-1) * inv.at(i) % mod;
		for(int i=1; i<d; i++) fac.at(i) = fac.at(i-1) * (k-i) % mod;
		ans = fac.at(d-1) * finv.at(d) % mod;
	}
	if(flg && (d==0)) ans = 1;
	cout << ans << endl;
	
}
### 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;

const int mod = pow(10,9)+7;

int main() {
	
	int x, y;
	cin >> x >> y;
	int k=x+y;
	bool flg = 1;
	if(k%3!=0) flg=0;
	k/=3;
	if(x<k || y<k) flg=0;
	int d = x-k;
	int ans = 0;
	if(flg && (d!=0)){
		vector<long long> inv(d+1),finv(d+1),fac(d);
		inv.at(1)=1;
		finv.at(1)=1;
		fac.at(0) = k;
		for(int i=2; i<=d; i++) inv.at(i) = mod - inv.at(mod%i) * (mod/i) %mod;
		for(int i=2; i<=d; i++) finv.at(i) = finv.at(i-1) * inv.at(i) % mod;
		for(int i=1; i<d; i++) fac.at(i) = fac.at(i-1) * (k-i) % mod;
		ans = fac.at(d-1) * finv.at(d) % mod;
	}
	if(flg && (d==0)) ans = 1;
	cout << ans << endl;
	
}
```