#include <bits/stdc++.h>
using namespace std;

long long MOD=1000000007LL;

long long fac[1000000],finv[1000000],inv[1000000];

void COMinit(){
	fac[0]=fac[1]=1;
	finv[0]=finv[1]=1;
	inv[1]=1;
	for(int i=2;i<1000000;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;
	}
}

long long COM(int n,int k){
	if(n<k)return 0;
	if(n<0 || k<0)return 0;
	return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

int zero(){
	cout << "0" << endl;
	return 0;
}

int main(){
	COMinit();
	int X,Y;
	cin >> X >> Y;
	
	if((X+Y)%3!=0)return zero();
	
	int N=(X+Y)/3;
	if(N>X || N>Y)return zero();
	
	X-=N;
	Y-=N;
	
	cout << COM(X+Y,X) << endl;
	
	return 0;
}
### 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>
using namespace std;

long long MOD=1000000007LL;

long long fac[1000000],finv[1000000],inv[1000000];

void COMinit(){
	fac[0]=fac[1]=1;
	finv[0]=finv[1]=1;
	inv[1]=1;
	for(int i=2;i<1000000;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;
	}
}

long long COM(int n,int k){
	if(n<k)return 0;
	if(n<0 || k<0)return 0;
	return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}

int zero(){
	cout << "0" << endl;
	return 0;
}

int main(){
	COMinit();
	int X,Y;
	cin >> X >> Y;
	
	if((X+Y)%3!=0)return zero();
	
	int N=(X+Y)/3;
	if(N>X || N>Y)return zero();
	
	X-=N;
	Y-=N;
	
	cout << COM(X+Y,X) << endl;
	
	return 0;
}
```