#include<cstdio>
#include<algorithm>
using namespace std;

const int MAX=700000;
const int MOD=1000000007;

long long fac[MAX],finv[MAX],inv[MAX];

void com(){
	fac[0]=fac[1]=1;
	finv[0]=finv[1]=1;
	inv[1]=1;
	for(int i=2;i<MAX;i++){
		fac[i]=fac[i-1]*i%MOD;
		inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
		finv[i]=finv[i-1]*inv[i]%MOD;
	}
}

//二項計算 nCk
long long comb(long long n,long long k){
	if(n<k)return 0;
	if(n<0||k<0)return 0;
	return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

int main(){
	com();
	long long  x,y;
	scanf("%lld%lld",&x,&y);
	if((x+y)%3!=0){
		printf("%d\n",0);
	}else{
		long long m,n;
		m=(2*y-x)/3;
		n=(2*x-y)/3;
		printf("%lld\n",comb(m+n,m));
	}
	return 0;
}
### Prompt

Please create a solution in CPP 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>
#include<algorithm>
using namespace std;

const int MAX=700000;
const int MOD=1000000007;

long long fac[MAX],finv[MAX],inv[MAX];

void com(){
	fac[0]=fac[1]=1;
	finv[0]=finv[1]=1;
	inv[1]=1;
	for(int i=2;i<MAX;i++){
		fac[i]=fac[i-1]*i%MOD;
		inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
		finv[i]=finv[i-1]*inv[i]%MOD;
	}
}

//二項計算 nCk
long long comb(long long n,long long k){
	if(n<k)return 0;
	if(n<0||k<0)return 0;
	return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

int main(){
	com();
	long long  x,y;
	scanf("%lld%lld",&x,&y);
	if((x+y)%3!=0){
		printf("%d\n",0);
	}else{
		long long m,n;
		m=(2*y-x)/3;
		n=(2*x-y)/3;
		printf("%lld\n",comb(m+n,m));
	}
	return 0;
}
```