#include <bits/stdc++.h>
const int N=1000005,mu=1000000007;
int p[N],inv[N],n,m,ans;
int ksm(int x,int y){
	int ans=1;
	for (;y;y>>=1,x=x*1ll*x%mu)
		if (y&1) ans=ans*1ll*x%mu;
	return ans;
}
int C(int x,int y){
	return p[x]*1ll*inv[y]%mu*inv[x-y]%mu;
}
int main(){
	scanf("%d%d",&n,&m);
	p[0]=1;
	for (int i=1;i<=n;i++) p[i]=p[i-1]*1ll*i%mu;
	inv[n]=ksm(p[n],mu-2);
	for (int i=n-1;i>=0;i--) inv[i]=inv[i+1]*1ll*(i+1)%mu;
	for (int i=0;i<=n/2;i++){
		int x=n-i*2;
		if (x*2+i==m){
			ans=(ans+C(x+i,i))%mu;
		}
	}
	printf("%d\n",ans);
}
### Prompt

Your challenge is to write 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>
const int N=1000005,mu=1000000007;
int p[N],inv[N],n,m,ans;
int ksm(int x,int y){
	int ans=1;
	for (;y;y>>=1,x=x*1ll*x%mu)
		if (y&1) ans=ans*1ll*x%mu;
	return ans;
}
int C(int x,int y){
	return p[x]*1ll*inv[y]%mu*inv[x-y]%mu;
}
int main(){
	scanf("%d%d",&n,&m);
	p[0]=1;
	for (int i=1;i<=n;i++) p[i]=p[i-1]*1ll*i%mu;
	inv[n]=ksm(p[n],mu-2);
	for (int i=n-1;i>=0;i--) inv[i]=inv[i+1]*1ll*(i+1)%mu;
	for (int i=0;i<=n/2;i++){
		int x=n-i*2;
		if (x*2+i==m){
			ans=(ans+C(x+i,i))%mu;
		}
	}
	printf("%d\n",ans);
}
```