#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int p=1000000007;
ll fast (ll d,ll z,ll m) {//快速幂
	ll ans=1;
	for (d%=m;z;ans=ans*(z&1?d:1)%m,z>>=1,d=d*d%m);
	return ans;
}
ll ni (int num) {
	return fast(num,p-2,p);
} 
int main () {
	ll a,b,x,y;
	cin>>a>>b;
	x=(2*a-b)/3;
	y=(2*b-a)/3;
	if (x<0||y<0||(a+b)%3!=0) {
		cout<<0;
	} else {
		ll ans=1,t=1,n=x+y,r=min(x,y);
		for (int i=0;i<r;i++) {
			ans=ans*(n-i)%p;
			t=t*(i+1)%p;
		}
		cout<<ans*ni(t)%p;
	}
}
### Prompt

Please formulate 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;
typedef long long ll;
int p=1000000007;
ll fast (ll d,ll z,ll m) {//快速幂
	ll ans=1;
	for (d%=m;z;ans=ans*(z&1?d:1)%m,z>>=1,d=d*d%m);
	return ans;
}
ll ni (int num) {
	return fast(num,p-2,p);
} 
int main () {
	ll a,b,x,y;
	cin>>a>>b;
	x=(2*a-b)/3;
	y=(2*b-a)/3;
	if (x<0||y<0||(a+b)%3!=0) {
		cout<<0;
	} else {
		ll ans=1,t=1,n=x+y,r=min(x,y);
		for (int i=0;i<r;i++) {
			ans=ans*(n-i)%p;
			t=t*(i+1)%p;
		}
		cout<<ans*ni(t)%p;
	}
}
```