#include <bits/stdc++.h>
#define MOD 1000000007
using namespace std;
long long fast(long long x,int k)
{
	if(k==0) return 1;
	long long c=fast(x,k/2);
	if(k%2==0) return (c*c)%MOD;
	return (((c*c)%MOD)*x)%MOD;
}
long long mmi(long long x) {return fast(x,MOD-2);}
long long fkt[1000007];
int main()
{
	int x,y; cin>>x>>y;
	if((x+y)%3!=0 || 2*y<x || 2*y-x>x+y) {printf("0"); return 0;}
	long long a=(2*y-x)/3,c=(x+y)/3;
	fkt[0]=1;
	for(long long i=1;i<=1000000;i++) fkt[i]=(fkt[i-1]*i)%MOD;
	cout<<(((fkt[c]*mmi(fkt[a]))%MOD)*mmi(fkt[c-a]))%MOD;
}
### Prompt

In CPP, your task is to solve 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>
#define MOD 1000000007
using namespace std;
long long fast(long long x,int k)
{
	if(k==0) return 1;
	long long c=fast(x,k/2);
	if(k%2==0) return (c*c)%MOD;
	return (((c*c)%MOD)*x)%MOD;
}
long long mmi(long long x) {return fast(x,MOD-2);}
long long fkt[1000007];
int main()
{
	int x,y; cin>>x>>y;
	if((x+y)%3!=0 || 2*y<x || 2*y-x>x+y) {printf("0"); return 0;}
	long long a=(2*y-x)/3,c=(x+y)/3;
	fkt[0]=1;
	for(long long i=1;i<=1000000;i++) fkt[i]=(fkt[i-1]*i)%MOD;
	cout<<(((fkt[c]*mmi(fkt[a]))%MOD)*mmi(fkt[c-a]))%MOD;
}
```