#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;
const int N=1e6+4;
ll inv[N];
double x,y;
inline void init() {
	inv[1]=1;
	for (register int i=2;i<N;i++)
		inv[i]=(MOD-(MOD/i))*inv[MOD%i]%MOD;
}
int main() {
	init();
	scanf("%lf%lf",&x,&y);
	double a=(x*2-y)/3,b=x-a*2;
	if (ceil(a)!=a||a<0||b<0) {
		puts("0");
		return 0;
	}
	int n=a+b;
	ll ans=1;
	for (register int i=1;i<=a;++i) {
		(ans*=(ll)(n-i+1))%=MOD;
		(ans*=inv[i])%=MOD;
	}
	printf("%lld\n",ans);
	return 0;
} 
### Prompt

Develop a solution in cpp 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<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<cmath>
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;
const int N=1e6+4;
ll inv[N];
double x,y;
inline void init() {
	inv[1]=1;
	for (register int i=2;i<N;i++)
		inv[i]=(MOD-(MOD/i))*inv[MOD%i]%MOD;
}
int main() {
	init();
	scanf("%lf%lf",&x,&y);
	double a=(x*2-y)/3,b=x-a*2;
	if (ceil(a)!=a||a<0||b<0) {
		puts("0");
		return 0;
	}
	int n=a+b;
	ll ans=1;
	for (register int i=1;i<=a;++i) {
		(ans*=(ll)(n-i+1))%=MOD;
		(ans*=inv[i])%=MOD;
	}
	printf("%lld\n",ans);
	return 0;
} 
```