#include<cstdio>
#define mod 1000000007
#define int long long
int x,y,fac[20010000];
int quickpow(int x,int y){
	if(y==0)return 1;
	if(y%2==0)return quickpow(x*x%mod,y/2);
	else return quickpow(x*x%mod,y/2)*x%mod;
}
int C(int n,int m){
	if(m==0||n==m)return 1;
	return fac[n]*quickpow(fac[m],mod-2)%mod*quickpow(fac[n-m],mod-2)%mod;
}
signed main(){
	scanf("%lld%lld",&x,&y);
	fac[0]=1;
	for(int i=1;i<=20000000;i++)
		fac[i]=fac[i-1]*i%mod;
	if((x+y)%3!=0)return puts("0"),0;
	if(2*y<x||2*x<y)return puts("0"),0;
	int X=(2*y-x)/3,Y=(2*x-y)/3;
	printf("%lld\n",C(X+Y,X));
}
### 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<cstdio>
#define mod 1000000007
#define int long long
int x,y,fac[20010000];
int quickpow(int x,int y){
	if(y==0)return 1;
	if(y%2==0)return quickpow(x*x%mod,y/2);
	else return quickpow(x*x%mod,y/2)*x%mod;
}
int C(int n,int m){
	if(m==0||n==m)return 1;
	return fac[n]*quickpow(fac[m],mod-2)%mod*quickpow(fac[n-m],mod-2)%mod;
}
signed main(){
	scanf("%lld%lld",&x,&y);
	fac[0]=1;
	for(int i=1;i<=20000000;i++)
		fac[i]=fac[i-1]*i%mod;
	if((x+y)%3!=0)return puts("0"),0;
	if(2*y<x||2*x<y)return puts("0"),0;
	int X=(2*y-x)/3,Y=(2*x-y)/3;
	printf("%lld\n",C(X+Y,X));
}
```