#include<bits/stdc++.h>
using namespace std;
#define mo 1000000007
#define maxn 1000000
#define LL long long
LL fac[maxn+5],inv[maxn+5];
LL C(int n,int m){
	return fac[n]*inv[m]%mo*inv[n-m]%mo;
}
void Pre(int p,LL a[],int n){
    a[0]=fac[1]=a[1]=1;
    for(int i=2;i<=n;i++){
    	fac[i]=1ll*fac[i-1]*i%p;
        a[i]=1ll*(p-p/i)*a[p%i]%p;
    }
    for(int i=2;i<=n;i++)a[i]=a[i]*a[i-1]%p;
}
int main(){
	Pre(mo,inv,maxn);
	int x,y;scanf("%d%d",&x,&y);
	if((x+y)%3)return puts("0"),0;
	if(y>2*x||x>2*y)return puts("0"),0;
	int t=(x+y)/3;
	x-=t,y-=t;;
	printf("%lld",C(x+y,x));
	return 0;
}
### Prompt

Your task is to create 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>
using namespace std;
#define mo 1000000007
#define maxn 1000000
#define LL long long
LL fac[maxn+5],inv[maxn+5];
LL C(int n,int m){
	return fac[n]*inv[m]%mo*inv[n-m]%mo;
}
void Pre(int p,LL a[],int n){
    a[0]=fac[1]=a[1]=1;
    for(int i=2;i<=n;i++){
    	fac[i]=1ll*fac[i-1]*i%p;
        a[i]=1ll*(p-p/i)*a[p%i]%p;
    }
    for(int i=2;i<=n;i++)a[i]=a[i]*a[i-1]%p;
}
int main(){
	Pre(mo,inv,maxn);
	int x,y;scanf("%d%d",&x,&y);
	if((x+y)%3)return puts("0"),0;
	if(y>2*x||x>2*y)return puts("0"),0;
	int t=(x+y)/3;
	x-=t,y-=t;;
	printf("%lld",C(x+y,x));
	return 0;
}
```