#include <iostream>

using namespace std;
typedef long long ll;
const int MAX = 2000100;
ll inv[MAX],fact[MAX],fi[MAX],mod = 1000000007;
void inverse(){
	int i;
	inv[1] = 1;
	for(i=2;i<MAX;i++){
		inv[i] = mod - (mod/i)*inv[mod%i]%mod;
	}
	fact[0] = fi[0] = 1;
	for(i=1;i<MAX;i++){
		fact[i] = fact[i-1]*i%mod;
		fi[i] = (fi[i-1]*inv[i])%mod;
	}
}

ll comb(int n,int k){
	if(n<0 || k<0 || n<k){
		return 0;
	}else{
		return fact[n]%mod*fi[k]%mod*fi[n-k]%mod;
	}
}
int main(){
	ll x,y;
	cin >> x >> y;
	if((x + y)%3!=0){
		cout << 0 << endl;
	}else{
		inverse();
		ll k = (2*x - y)/3,l = (2*y - x)/3;
		cout << comb(k + l,l) << endl;
	}
}
### Prompt

Create a solution in CPP for 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;
typedef long long ll;
const int MAX = 2000100;
ll inv[MAX],fact[MAX],fi[MAX],mod = 1000000007;
void inverse(){
	int i;
	inv[1] = 1;
	for(i=2;i<MAX;i++){
		inv[i] = mod - (mod/i)*inv[mod%i]%mod;
	}
	fact[0] = fi[0] = 1;
	for(i=1;i<MAX;i++){
		fact[i] = fact[i-1]*i%mod;
		fi[i] = (fi[i-1]*inv[i])%mod;
	}
}

ll comb(int n,int k){
	if(n<0 || k<0 || n<k){
		return 0;
	}else{
		return fact[n]%mod*fi[k]%mod*fi[n-k]%mod;
	}
}
int main(){
	ll x,y;
	cin >> x >> y;
	if((x + y)%3!=0){
		cout << 0 << endl;
	}else{
		inverse();
		ll k = (2*x - y)/3,l = (2*y - x)/3;
		cout << comb(k + l,l) << endl;
	}
}
```